# Worksheet: Isothermal

In this worksheet, we will practice relating the net work done on, the heating of, and the change in internal energy of a gas with varying pressure and/or volume.

**Q3: **

Two moles of helium gas are placed in a cylindrical container with a movable lid held in place by a piston. The gas is at a temperature of and at a pressure of Pa. The pressure supplied by the piston is decreased but the temperature of the gas does not change. The volume of the gas doubles.

Find the work done by the piston on the gas during the expansion.

How much heat enters the gas? Assume ideal gas behavior.

**Q4: **

It is found that, when a dilute gas expands quasi-statically from a volume of 0.53 L to a volume of 6.20 L, the gas does 480 J of work. Assuming that the gas temperature remains constant at 330 K, how many moles of the gas’s molecules are contained in the gas?

- A3.2 moles
- B0.85 moles
- C1.5 moles
- D0.022 moles
- E0.071 moles

**Q7: **

When a dilute gas expands quasi-statically from a volume of 0.250 L to a volume of 6.400 L, the gas does 295 J of work. The gas temperature remains constant at 310 K.

How many moles of the gas’s molecules does the gas contain?

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

How much is the gas heated?

**Q8: **

3.0 moles of a monatomic ideal gas in a conducting container with a movable piston is placed in a large thermal heat bath at temperature 420 K and the gas is allowed to come to equilibrium. After the equilibrium is reached, the pressure on the piston is lowered so that the gas expands at constant temperature. The process is continued quasi-statically until the final pressure is exactly of the initial pressure.

Find the change in the internal energy of the gas.

Find the work done by the gas.

How much was the gas heated by the heat bath?