Connected Containers: Problems:

(1) Two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are P_A, T_A and V in the vessel A and P_B , T_B and V in vessel B . the vessels are now connected through a small tube. P/T value is equal to.

(2) Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure Pi and temperature Ti are connected through a narrow tube of negligible volume as shown in the figure below. The pressure of one of the bulb is raised to T2. The final pressure is: (JEE Mains-2016)

(3) A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure 2), the volume (in m3) of the compartment A after the system attains equilibrium is--- (IIT-Ad-2018)

(4) The stop-cock connecting the two bulbs of 5dm3 and 10dm3 contains an ideal gas at 10 bar and 10 bar respectively is opened. Thus final pressure if two bulbs opened at the same temperature is

(5)Two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are P_A, T_A and V in the vessel A and P_B , T_B and V in vessel B . the vessels are now connected through a small tube. P/T value is equal to.

Two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are P_A, T_A and V in the vessel A and P_B , T_B and V in vessel B . the vessels are now connected through a small tube. P/T value is equal to.

Payload is defined as the difference between the mass of the displaced air and the mass of the balloon. Calculate the payload when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at 27°C. (Density of air = 1.2 kgm-3 and R = 0.083 bar dm3 K-1 mol-1)

One mole of a gas is expanded from (2 L, 20 atm,300K) to (5 L, 10 atm,320K) against a constant external pressure of 5 atm. The heat capacity of gas is 100 J/K.Then the enthalpy change during the process is (1 L atm ≃ 100 J)

A certain mass of gas is expanded from (1L,10 atm) to (4L,5 atm) against a constant external pressure of 1 atm. If the initial temperature of the gas is 300 K and the heat capacity of the process is 50 J/∘C. Then the enthalpy change during the process is: (1L atm≃100 J).

The equation of state for a gas is P(V−nb)=nRT, where b and R are constants. If the pressure and temperature are such that V m​ =10b, what is the compressibility factor of gas in this condition?

A 10 liter container consist of 1 mole of gas at 300 K. It is connected to another container having volume 40 liter and is initially at 300 K. The nozzle connecting two containers is opened for a long time and once the movement of gas stopped, the larger container was heated to a temperature of 600 K. Calculate

(A) Moles and pressure of gas in both the containers before heating. (B) Moles and pressure in two containers after heating. Assume that initially the larger container is completely evacuated.

Find out the ratio of the moles of hydrogen and carbon dioxide obtained after 6 successive effusion step initially present in 1:1 molar ratio

Answer Key: 22^6

An air bubble starts rising from the bottom of lake, it diameter is 3.6 mm at bottom and 4 mm at the surface. The depth of lake is 250 cm and temperature at surface is 40℃ . What is the temperature at the bottom of lake? (Given atmospheric pressure = 76 cm of Hg and g= 980 cm sec-1 neglect surface tension effect).

A bubble of gas released at bottom. of the lake increase to four time its original volume when it reach the surface. assuming that atmosphere ic pressure is equivalent to the exerted by a column of water 10 m height. What is the depth of the lake.

Radius of bubble X-1 is 0.32 cm and X-2 is 0.48 cm. What is the temperature of of pond at the position of bubble X-2. If presure of the Bottom of the pond is 2.8 atm and at the top is 1 atm.

(A) 40℃

(B) 50℃

(C) 60℃

(D) 70℃

Ans Key: (C) 60℃

Related Questions:

(1) The diameters of a bubble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm and the temperature of the lake-water and the atmosphere are equal what is the depth of the lake ? (The density of lake-water and Hg are 1 gm/ml and 13.6 respectively. Also neglect the contribution of pressure due to surface tension)

How to calculate Payload of a Balloon?

Payload of a Balloon if defined as maximum mass which a Balloon can carry with in it upward direction.

If V is the volume of Balloon , d_out is the density of out side air , d_in is the density of gas inside of Balloon  and Maas of Balloon is m then

Payload= [d_out × V]- [d-in×V+m]

Related Questions;

(1) Calculate payload of a balloon having volume 100 litre. It is filled with helium gas at 0.2486 atm pressureand 300K. Density of air is 1.3 gm/litre and mass of material of balloon is 20 gm.

(2) A balloon of diameter 20 m weighs 100 kg. Calculate its paylod if it is filled with helium at 1.0 atm and 27 ∘ C. Density of air is 1.2 kg m −3 .(R=0.082 dm 3 atm K −1 mol −1 ).

Air Bubbles in water, or lake temperature, lake depth, related Questions.

(1) The diameters of a buble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm and the temperature of the lake-water and the atmosphere are equal what is the depth of the lake ? (The density of lake-water and Hg are 1 gm/ml and 13.6 respectively. Also neglect the contribution of pressure due to surface tension)

(2) Radius of bubble X-1 is 0.32 cm and X-2 is 0.48 cm. What is the temperature of of pond at the position of bubble X-2. If presure of the Bottom of the pond is 2.8 atm and at the top is 1 atm.

(3) A bubble of gas released at bottom. of the lake increase to four time its original volume when it reach the surface. assuming that atmosphere ic pressure is equivalent to the exerted by a column of water 10 m height. What is the depth of the lake.

(4) An air bubble starts rising from the bottom of lake, it diameter is 3.6 mm at bottom and 4 mm at the surface. The depth of lake is 250 cm and temperature at surface is 40℃ . What is the temperature at the bottom of lake? (Given atmospheric pressure = 76 cm of Hg and g= 980 cm sec-1 neglect surface tension effect).

The States of matter : Numerical Questions : Part-(2):

(1) The rms speed of an ideal gas at 27°C is 0.3 ms–1 . Its rms speed at 927°C (in ms–1) is

(2) The compressibility factor for 1 mole of a van der Waals gas at 0oC and 100 atm pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant, a.

(3) Two moles of ammonia gas are enclosed in a vessel of 5 litre capacity at 27oC. Calculate the pressure exerted by the gas, assuming that (i) the gas behaves like an ideal gas (using ideal gas equation). (ii) the gas behaves like a real gas (using van der Waal’s equation). Given that for ammonia, a = 4.17 atm litre2 mol–2 and b = 0.037 litre mol–1

(4) 1 mole of CCl4 vapours at 77oC occupies a volume of 35.0 L. If vander waal’s constants are a = 20.39 L 2 atm mol–2 and b = 0.1383 L mol–1, calculate compressibility factor Z under (a) low pressure region. (b) high pressure region.

(5) What is Vander waals equation of state of a real gas ?

(6) Calculate the mass of mercuryin a uniform column, 760 mm high and 1.00 cm2 in cross-sectional area. Is there any change in (a) mass and (b) pressure of column of same height but with 2.00 cm2 cross sectional area is taken ? (density of Hg = 13.6 g/cm3 )

(7) A sample of a given mass of a gas at a constant temperature occupies 95cm3 under a pressure of 9.962 × 104N/m2 .At the same temperature, it volume at a pressure of 10.13 × 104 N/m2 is :

(8) A gas occupied a volume of 250 ml at 700 mm Hg pressure and 25°C. What additional pressure is required to reduce the gas volume to its 4/5th value at the same temperature

(9) Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.the

(10) Why liquid have a definite volume but no definite shape?

The States of matter : Numerical Questions : Part-(1):

(1) What is Boyle's temperature ? and what is relation of Boyle's temperature with Vander waal's constant?

(2) A 10 cm column of air is trapped by a column of Hg, 8 cm long, in a capillary tube horizontally fixed as shown below, at 1 atm pressure. Calculate the length of air column when the tube is fixed at the same temperature 

(a) vertically with open end up

(b) vertically with open end down (c) At 45° from vertical, with open end up.

(3) What is payload of Balloon ?

(4) Calculate payload of a balloon having volume 100 litre. It is filled with helium gas at 0.2486 atm pressureand 300K. Density of air is 1.3 gm/litre and mass of material of balloon is 20 gm.

(5) A balloon of diameter 20 m weighs 100 kg. Calculate its paylod if it is filled with helium at 1.0 atm and 27 ∘ C. Density of air is 1.2 kg m −3 .(R=0.082 dm 3 atm K −^1 mol ^−1 ).

(6) What is Aqueous tension ?

(7) The diameters of a buble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm, what is the depth of the lake ? The density of lake-water and Hg are 1.0 gm/ml and 13.6 gm/ml, respectively. Assume that temperature of lake water is equal to that of atmosphere.Also neglect the contribution of pressure due to surface tension.

(8) Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

(9) In a barometeric tube Hg is replaced by H2O then find the height of H2O column to measure the atmospheric pressure.Assume that vapour pressure of H2O in negligible.

(10) An open vessel at 27℃ is heated at constant pressure until 3/5th of the air in it has been expelled. Find 

(a) the temperature at which vessel was heated ? 

(b) the moles of air eascaped out, if vessel were heated to 900 K ?

(c) temperature at which half of the air escapes out ?

(11) When 3.2 g of sulphur is vapourised at 450°C and 723 mm pressure, the vapours occupy a volume of 780 ml. What is the molecular formula of sulphur vapours under these conditions?

(12) A spherical balloon of 21 cm diameter is to be filled up with hydrogen at 0℃ and 1 atm from a cylinder containing the gas at 20 atmosphere at 27℃. If the cylinder can hold 2.82 litre of water at 0℃ and 1 atm, calculate the number of balloon that can be filled up.

(13) The density of methane at 2.0 atmosphere pressure and 27°C is

(14) A mixture of CO and CO2 is found to have a density of 1.50 g/litre at 30℃ and 730 mm. The mole percent of CO in the mixture is

(15) A vessel of 2 lit. capacity contains hydrogen at 380 mm pressure at 27°C. 16 gm of O2 is added to the container at constant temperature, then find the final total pressure and final partial pressure of H2 . Sol. As partial pressure of a gas is independent from the pressure of other gas, initial as well as final partial pressue of H2 gas,

(16) 1 mole of N2 and 3 moles of H2 are mixed in 8.21 lit. container at 300 K to form NH3 . If at equilibrium, average molecular mass was found to be 34/3, then find partial pressure of each component.

(17) One litre flask contains air, water vapour and a small amount of liquid water at a pressure of 200 mmHg. If this is connected to another one-litre evacuated flask, what will be the final pressure of the gas mixture at equilibrium?Assume the temperature to be 50°C.Aqueous tension at 50°C = 93 mm Hg.

(18) A sample of butane gas C4H10 of unknown mass is contained in a vessel of unknown volume V at 25oC and a pressure of 760 mmHg. To this vessel 8.6787 g of neon gas is added in such a waythat no butane is lost from the vessel. The final pressure in the vessel is 1920 mm Hg at the same temperature. Calculate the volume of the vessel and the mass of butane.

(19) What are the difference between Diffusion and Effusion ?

(20) The rms speed of CO2 at a temperature T (in kelvin) is x cm s–^1.At what temperature (in kelvin) the rms speed of nitrous oxide would be 4x cm s^–1 ?

The diameters of a buble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm and the temperature of the lake-water and the atmosphere are equal what is the depth of the lake ? (The density of lake-water and Hg are 1 gm/ml and 13.6 respectively. Also neglect the contribution of pressure due to surface tension)

 Related questions:

(1) Liquid ammonia bottle is cooled before opening the seal. Explain.

(2)The molecular speeds of gaseous molecules are analogous to those of rifle bullets; why is then odour of the gaseous molecule not detected so fast?

(3) Carbon dioxide is heavier than oxygen and nitrogen but is does not form the lower layer of the atmosphere. Explain.

(4) Out of dry air and wet air, which is heavier?

(5) Can we apply Dalton’s law of partial pressure to a mixture of carbon monoxide and oxygen?

(6) Why a bottle of liquid ammonia is cooled before opening the seal?

(7) Explain , Aerated water bottles are kept under water during summer why?

(8) Arrange the following in the increasing order of melting point of different types of crystalline solid (i) Covalent solid (ii) Metallic solid (iii) Molecular (iv) Ionic

(9) Why falling liquid drops are spherical?

(10) Why diethyl ether has higher vapour pressure than ethyl alcohol at a particular temperature?

(11) Why liquid have a definite volume but no definite shape?

(12)What are the difference between Diffusion and Effusion ?

(12) What is payload of Balloon ?

(13)What is Aqueous tension ?

(14) What is Vander waals equation of state of a real gas ?

(15) What is Boyle's temperature ? and what is relation of Boyle's temperature with Vander waal's constant?

Equal moles of hydrogen and oxygen gases are placed in a container with a pin-hole through which both can escape. What fraction of the oxygen escapes in the time required for one- half of the hydrogen to escape.

Related Questions;

(1) Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure Pi and temperature Ti are connected through a narrow tube of negligible volume as shown in the figure below. The pressure of one of the bulb is raised to T2. The final pressure is: (JEE Mains-2016)

(2) A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure 2), the volume (in m3) of the compartment A after the system attains equilibrium is--- (IIT-Ad-2018)

(3) A sample of butane gas C4H10 of unknown mass is contained in a vessel of unknown volume V at 25oC and a pressure of 760 mmHg. To this vessel 8.6787 g of neon gas is added in such a waythat no butane is lost from the vessel. The final pressure in the vessel is 1920 mm Hg at the same temperature. Calculate the volume of the vessel and the mass of butane.

(4) One litre flask contains air, water vapour and a small amount of liquid water at a pressure of 200 mmHg. If this is connected to another one-litre evacuated flask, what will be the final pressure of the gas mixture at equilibrium?Assume the temperature to be 50°C.Aqueous tension at 50°C = 93 mm Hg.

(5) 1 mole of N2 and 3 moles of H2 are mixed in 8.21 lit. container at 300 K to form NH3 . If at equilibrium, average molecular mass was found to be 34/3, then find partial pressure of each component.

(6) A vessel of 2 lit. capacity contains hydrogen at 380 mm pressure at 27°C. 16 gm of O2 is added to the container at constant temperature, then find the final total pressure and final partial pressure of H2 . Sol. As partial pressure of a gas is independent from the pressure of other gas, initial as well as final partial pressue of H2 gas,

(7) A mixture of CO and CO2 is found to have a density of 1.50 g/litre at 30oC and 730 mm. The mole percent of CO in the mixture is

The stop-cock connecting the two bulbs of 5dm3 and 10dm3 contains an ideal gas at 10 bar and 10 bar respectively is opened. Thus final pressure if two bulbs opened at the same temperature is

 At constant temperature

P₁V₁+P₂V₂ =P_R(V₁+V₂)   

5x10 +10x5 = P_R(5+10)

P_R= 100/15 =6.67 bar.

Related Questions;

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure Pi and temperature Ti are connected through a narrow tube of negligible volume as shown in the figure below. The pressure of one of the bulb is raised to T2. The final pressure is: (JEE Mains-2016)

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure 2), the volume (in m3) of the compartment A after the system attains equilibrium is--- (IIT-Ad-2018)

A sample of butane gas C4H10 of unknown mass is contained in a vessel of unknown volume V at 25oC and a pressure of 760 mmHg. To this vessel 8.6787 g of neon gas is added in such a waythat no butane is lost from the vessel. The final pressure in the vessel is 1920 mm Hg at the same temperature. Calculate the volume of the vessel and the mass of butane.

One litre flask contains air, water vapour and a small amount of liquid water at a pressure of 200 mmHg. If this is connected to another one-litre evacuated flask, what will be the final pressure of the gas mixture at equilibrium?Assume the temperature to be 50°C.Aqueous tension at 50°C = 93 mm Hg.

1 mole of N2 and 3 moles of H2 are mixed in 8.21 lit. container at 300 K to form NH3 . If at equilibrium, average molecular mass was found to be 34/3, then find partial pressure of each component.

A vessel of 2 lit. capacity contains hydrogen at 380 mm pressure at 27°C. 16 gm of O2 is added to the container at constant temperature, then find the final total pressure and final partial pressure of H2 . Sol. As partial pressure of a gas is independent from the pressure of other gas, initial as well as final partial pressue of H2 gas,

A mixture of CO and CO2 is found to have a density of 1.50 g/litre at 30oC and 730 mm. The mole percent of CO in the mixture is

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure Pi and temperature Ti are connected through a narrow tube of negligible volume as shown in the figure below. The pressure of one of the bulb is raised to T2. The final pressure is: (JEE Mains-2016)

 

Initially both bulbs are under similar condition hence number of moles of gas in each container

Total number of moles in both bulbs;

When temperature of one of the bulb is increases from T₁ toT₂ then final pressure P_f  and number of moles.  

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure 2), the volume (in m3) of the compartment A after the system attains equilibrium is--- (IIT-Ad-2018)

Total volume of compartment A and B

 V_A+V_B = 4m³…………………………………….................................(1)

According to question partition do not allow gas leak between compartment (A) and compartment (B) so number of moles after and before inserting new partition which can slide.

So number of moles in compartment (A) and compartment (B)

n_A=PxV_A/RT=1m³x5 bar/400 K  ……………………………………… (2)

n_B=PxV_B/RT=3m³x1 bar/300 K  ………………………………………. (3)

Equation (2)/ (3)

Get V_A/V_B=5/4   Or  V_A=5V_B/4 ………………………………………..(4)

Put the value of V_A   from equation (4) to in equation (1) and find the value of V_A  after placing frictionless slider.

5V_B/4 +V_B = 4m³        => V_B = 16/9m³       and  V_A = 20/9m³   =2.22  m³  or L

Related Questions:

Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

A gas occupied a volume of 250 ml at 700 mm Hg pressure and 25°C. What additional pressure is required to reduce the gas volume to its 4/5th value at the same temperature

A sample of a given mass of a gas at a constant temperature occupies 95cm3 under a pressure of 9.962 × 104N/m2 .At the same temperature, it volume at a pressure of 10.13 × 104 N/m2 is :

Calculate the mass of mercuryin a uniform column, 760 mm high and 1.00 cm2 in cross-sectional area. Is there any change in (a) mass and (b) pressure of column of same height but with 2.00 cm2 cross sectional area is taken ? (density of Hg = 13.6 g/cm3 )

1 mole of CCl4 vapours at 77oC occupies a volume of 35.0 L. If vander waal's constants are a = 20.39 L 2 atm mol–2 and b = 0.1383 L mol–1, calculate compressibility factor Z under (a) low pressure region. (b) high pressure region.

Two moles of ammonia gas are enclosed in a vessel of 5 litre capacity at 27oC. Calculate the pressure exerted by the gas, assuming that (i) the gas behaves like an ideal gas (using ideal gas equation). (ii) the gas behaves like a real gas (using van der Waal's equation). Given that for ammonia, a = 4.17 atm litre2 mol–2 and b = 0.037 litre mol–1

The compressibility factor for 1 mole of a van der Waals gas at 0oC and 100 atm pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant, a.

The rms speed of an ideal gas at 27°C is 0.3 ms–1 . Its rms speed at 927°C (in ms–1) is

The rms speed of CO2 at a temperature T (in kelvin) is x cm s–1.At what temperature (in kelvin) the rms speed of nitrous oxide would be 4x cm s–1 ?

A sample of butane gas C4H10 of unknown mass is contained in a vessel of unknown volume V at 25oC and a pressure of 760 mmHg. To this vessel 8.6787 g of neon gas is added in such a waythat no butane is lost from the vessel. The final pressure in the vessel is 1920 mm Hg at the same temperature. Calculate the volume of the vessel and the mass of butane.

One litre flask contains air, water vapour and a small amount of liquid water at a pressure of 200 mmHg. If this is connected to another one-litre evacuated flask, what will be the final pressure of the gas mixture at equilibrium?Assume the temperature to be 50°C.Aqueous tension at 50°C = 93 mm Hg.

1 mole of N2 and 3 moles of H2 are mixed in 8.21 lit. container at 300 K to form NH3 . If at equilibrium, average molecular mass was found to be 34/3, then find partial pressure of each component.

A vessel of 2 lit. capacity contains hydrogen at 380 mm pressure at 27°C. 16 gm of O2 is added to the container at constant temperature, then find the final total pressure and final partial pressure of H2 . Sol. As partial pressure of a gas is independent from the pressure of other gas, initial as well as final partial pressue of H2 gas,

A mixture of CO and CO2 is found to have a density of 1.50 g/litre at 30oC and 730 mm. The mole percent of CO in the mixture is

The density of methane at 2.0 atmosphere pressure and 27°C is

A spherical balloon of 21 cm diameter is to be filled up with hydrogen at 0oC and 1 atm from a cylinder containing the gas at 20 atmosphere at 27oC. If the cylinder can hold 2.82 litre of water at 0oC and 1 atm, calculate the number of balloon that can be filled up.

When 3.2 g of sulphur is vapourised at 450°C and 723 mm pressure, the vapours occupy a volume of 780 ml. What is the molecular formula of sulphur vapours under these conditions?

An open vessel at 27oC is heated at constant pressure until 3/5th of the air in it has been expelled. Find (a) the temperature at which vessel was heated ? (b) the moles of air eascaped out, if vessel were heated to 900 K ? (c) temperature at which half of the air escapes out ?

In a barometeric tube Hg is replaced by H2O then find the height of H2O column to measure the atmospheric pressure.Assume that vapour pressure of H2O in negligible.

Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

The diameters of a buble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm, what is the depth of the lake ? The density of lake-water and Hg are 1.0 gm/ml and 13.6 gm/ml, respectively. Assume that temperature of lake water is equal to that of atmosphere.Also neglect the contribution of pressure due to surface tension.

A balloon of diameter 20 m weighs 100 kg. Calculate its paylod if it is filled with helium at 1.0 atm and 27 ∘ C. Density of air is 1.2 kg m −3 .(R=0.082 dm 3 atm K −1 mol −1 ).

Calculate payload of a balloon having volume 100 litre. It is filled with helium gas at 0.2486 atm pressureand 300K. Density of air is 1.3 gm/litre and mass of material of balloon is 20 gm.

A 10 cm column of air is trapped by a column of Hg, 8 cm long, in a capillary tube horizontally fixed as shown below, at 1 atm pressure. Calculate the length of air column when the tube is fixed at the same temperature (a) vertically with open end up (b) vertically with open end down (c) At 45° from vertical, with open end up.