In this worksheet, we will practice relating the net work done on and the change in internal energy of a gas with varying bulk properties but zero net heating.

**Q1: **

In a diesel engine, the fuel is ignited without a spark plug. Instead, air in a cylinder is compressed adiabatically to a temperature above the ignition temperature of the fuel; at the point of maximum compression, the fuel is injected into the cylinder. Air at a temperature of is taken into the cylinder at a volume and then compressed adiabatically and quasi-statically to a temperature of and a volume . If the ratio of the molar heat capacities of the gas is 1.4, what is the ratio ?

**Q2: **

An ideal diatomic gas at a temperature of is slowly compressed adiabatically and reversibly to half its initial volume. What is its absolute temperature after compression?

**Q3: **

A monatomic ideal gas with an initial volume undergoes a quasi-static adiabatic expansion. The volume of the gas after its expansion is . If the pressure of the gas before expansion is , what fraction of does the gasses expansion reduce its pressure by?

**Q4: **

An insulated vessel contains 1.5 moles of argon at 2.0 atm. The gas initially occupies a volume of 5.0 L. As a result of the adiabatic expansion the pressure of the gas is reduced to 1.0 atm.

Find the volume of the final state.

Find the temperature of the final state.

Find the temperature of the gas in the initial state.

Find the work done by the gas in the process.

Find the change in the internal energy of the gas in the process.

**Q5: **

In an adiabatic process, oxygen gas in a container is compressed along a path that can be described by the following pressure in atm as a function of volume, , with . The initial and final volumes during the process were 2.0 L and 1.5 L, respectively. The specific heat ratio for oxygen is 1.395. Find the amount of work done on the gas.

**Q6: **

Three moles of a diatomic ideal gas is compressed adiabatically and reversibly from a state where its pressure is 4.0 atm and its volume is 6.0 L to a state where its pressure is 7.0 atm.

What is the temperature of the initial state of the gas?

What is the volume of the final state of the gas?

What is the temperature of the final state of the gas?

What is the work done by the gas in the process?

What is the change in the internal energy of the gas in the process?

**Q8: **

3.0 moles of an ideal
monatomic gas occupy a volume of m^{3} at a pressure of
N/m^{2}. The gas undergoes a quasi-static
adiabatic compression until its volume is decreased to m^{3}.

What is the temperature of the gas before it is compressed?

What is the temperature of the gas after it is compressed?

How much work is done on the gas during the compression?

What is the change in the internal energy of the gas?

**Q9: **

2.0 moles of a monatomic ideal gas are compressed adiabatically and reversibly from a state where the pressure is 4.0 atm and the volume is 9.0 L to a state with a pressure of 2.0 atm.

Find the volume of the gas in its final state.

Find the temperature of the gas in its final state.

Find the work done by the gas in the process.

Find the change in internal energy in the process. Assume that the molar heat capacity at constant volume and that the molar heat capacity at constant pressure for the monatomic ideal gas in the conditions given.

**Q11: **

A gas in a cylindrical closed container is adiabatically and quasi-statically expanded from a state where it is at a pressure of 3.00 MPa and has a volume of 2.00 L, to a state with volume of 6.00 L along the path .

Find the amount of work done by the gas.

Find the change in the internal energy of the gas during the process.

**Q12: **

What is an adiabatic process?

- AA process in which the pressure stays constant.
- BA process in which the temperature stays constant.
- CA process in which the volume of the system stays constant.
- DA process in which the system is perfectly insulated and heat transfer is zero.
- EA process in which the entropy does not change.

**Q13: **

In an adiabatic turbine, water vapor at a temperature of 573 K and a pressure of 2.00 MPa is expanded until its pressure is 0.0300 MPa. What is the magnitude of work done per kg of vapor?