## Adiabatic changes problems

1. Air at 20 °C is allowed to expand under adiabatic conditions until its pressure has fallen to one-third of its original value.

What is the final temperature of the air? (Ratio of the principal specific heats of air = 1.4)

2. A certain volume of helium at 15°C is expanded adiabatically until its volume is trebled.

Calculate the temperature of the gas immediately after the expansion has taken place. (Ratio of the principal specific heat capacities of helium = 1.67)

3. Some nitrogen at 20°C is expanded isothermally to twice its original volume. It is then cooled at constant volume to -10°C and finally compressed adiabatically to its original pressure and volume.

(a) Draw a pV diagram to show this change.

(b) Calculate the pressure after the isothermal expansion.

(c) Calculate the pressure after the cooling at constant volume.

4. The density of neon at 27°C and a pressure of 1.00x10

5. Two identical glass bulbs are joined with a thin glass tube and filled with air which is initially at 20°C. What will the pressure in the apparatus become if one bulb is immersed in steam and the other in melting ice?

6. When a gas expands adiabatically it does work on its surroundings although there is no heat input to the gas. Where does this energy come from?

7. A mass of 1 g of hydrogen at 20°C and 10

8. A mass of air with an initial volume of 5 litres at a temperature of 0°C and a pressure of 10

Show the process on a PV diagram and calculate the final pressure and temperature of the air. At what volume was the pressure momentarily atmospheric? (Assume γ for air = 1.40.)

9. State the first law of thermodynamics. How is the equation modified for: (a) an adiabatic change

(b) an input of heat at constant volume. Explain how the composition of the term for internal energy for a real gas differs from that for an ideal one.

What is the final temperature of the air? (Ratio of the principal specific heats of air = 1.4)

2. A certain volume of helium at 15°C is expanded adiabatically until its volume is trebled.

Calculate the temperature of the gas immediately after the expansion has taken place. (Ratio of the principal specific heat capacities of helium = 1.67)

3. Some nitrogen at 20°C is expanded isothermally to twice its original volume. It is then cooled at constant volume to -10°C and finally compressed adiabatically to its original pressure and volume.

(a) Draw a pV diagram to show this change.

(b) Calculate the pressure after the isothermal expansion.

(c) Calculate the pressure after the cooling at constant volume.

4. The density of neon at 27°C and a pressure of 1.00x10

^{5}Pa is 0.90 kgm^{-3}. Calculate the mass of neon in a neon discharge tube of volume 250 cm^{3}if the pressure inside it is 1.00x10^{5}Pa at a temperature of 150 °C5. Two identical glass bulbs are joined with a thin glass tube and filled with air which is initially at 20°C. What will the pressure in the apparatus become if one bulb is immersed in steam and the other in melting ice?

6. When a gas expands adiabatically it does work on its surroundings although there is no heat input to the gas. Where does this energy come from?

7. A mass of 1 g of hydrogen at 20°C and 10

^{5}Pa has its volume halved by an adiabatic change. Calculate the change in the internal energy of the gas. (Ideal gas constant = 8.31 J mol^{-1}; ratio of .the principal specific heats for hydrogen = 1.40)8. A mass of air with an initial volume of 5 litres at a temperature of 0°C and a pressure of 10

^{5}Pa is compressed isothermally to 2.5 litres, and then allowed to expand adiabatically to 12.5 litres.Show the process on a PV diagram and calculate the final pressure and temperature of the air. At what volume was the pressure momentarily atmospheric? (Assume γ for air = 1.40.)

9. State the first law of thermodynamics. How is the equation modified for: (a) an adiabatic change

(b) an input of heat at constant volume. Explain how the composition of the term for internal energy for a real gas differs from that for an ideal one.