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.

Q1:

An ideal gas expands quasi-statically to twice its original volume. Determine the ratio of the work done in an isothermal expansion to the work done in an isobaric expansion.

  • A l n 4
  • B l n 2
  • C1
  • D l n 3
  • E l n 0 . 5

Q2:

0.50 mol of an ideal gas is quasi-statically compressed at constant temperature. The volume of the gas after compression 𝑉 is 0.20 𝑉, where 𝑉 is the initial volume of the gas. Calculate the temperature of the gas if 5.0×10 J of work was done to compress it.

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 25∘C and at a pressure of 3.0×10 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

Q5:

An ideal gas expands quasi-statically and isothermally from a state with pressure 2.2 bar and volume 0.85 L to a state with volume 1.70 L. How much heat is added to the expanding gas?

Q6:

9.0 moles of a monatomic ideal gas in a cylinder at a temperature of 52∘C was expanded isothermally from a volume of 4.7 L to a volume of 12.0 L.

What was the change in the gas’s internal energy?

How much work was done on the gas in the process?

How much was the gas heated?

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 25 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?

Q9:

1.00 mol of an ideal gas at a pressure of 3.00 atm and a temperature of 300 K expands isothermally to exactly triple its volume. What is the work done by the gas due to its expansion?

Q10:

In an isothermal reversible expansion of an ideal gas at a temperature of 25∘C, the gas does 25 J of work. What is the entropy change of the gas?

Q11:

An ideal gas initially at a temperature of −21.0∘C and a pressure of 33.4 kPa is compressed isothermally to a pressure of 159 kPa. Calculate the magnitude of work done by 2.00 moles of gas in this process.

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