# Worksheet: Heat Capacities of Gasses

In this worksheet, we will practice relating changes of a gas’s bulk properties to its specific heat capacity and defining the first law of thermodynamics.

**Q2: **

3.0 mol of a dilute monatomic gas, 0.50 mol of a dilute diatomic gas, and 15 mol of a dilute polyatomic gas are initially at K. The temperature of each gas is increased by when they are heated. Assuming the gases are ideal.

What is the change in internal energy of the 3.0 mol of dilute monatomic gas after it is heated?

What is the change in internal energy of the 0.50 mol of dilute diatomic gas after it is heated?

What is the change in internal energy of the 15 mol of dilute polyatomic gas after it is heated?

**Q4: **

6.0 mol of a dilute monatomic gas, 0.75 mol of a dilute diatomic gas, and 25 mol of a dilute polyatomic gas have their temperatures increased from room temperature by , at constant volume.

Determine the heating of the 6.0 mol of dilute monatomic gas.

Determine the heating of the 0.75 mol of dilute diatomic gas.

Determine the heating of the 25 mol of dilute polyatomic gas.

**Q5: **

A room that is modeled as perfectly rigid and perfectly insulating has a volume of
35 m^{3}. The room is
filled with air, modeled to be diatomic, at a temperature of
and a pressure
of Pa.
A block of ice of mass 1.35 kg
that is at a temperature of
is placed in
the room. What is the equilibrium temperature of the ice and air? Use a value of
for the specific heat capacity of water and use a value of
334 kJ/kg for the heat of fusion of ice.

**Q6: **

In car racing, one advantage of mixing liquid nitrous oxide () with air is that the boiling of the nitrous absorbs latent heat of vaporization and thus cools the air and ultimately the fuel-air mixture, allowing more fuel-air mixture to go into each cylinder. 1.0 mol of nitrous oxide gas at its boiling point of is mixed with 4.0 mol of air at a temperature of . What is the final temperature of the mixture? Use a value of for the specific heat capacity of at . Model air as a diatomic gas.

**Q7: **

Professional divers sometimes use heliox, which is a mixture by mole of helium and oxygen. A perfectly rigid scuba tank with a volume of 15 L contains heliox at an absolute pressure of Pa and at a temperature of .

Determine how many moles of helium are in the tank. Use a value of 4.003 g/mol for the molar mass of helium.

How many moles of oxygen are in the tank?

The diver descends to a point where the sea temperature is while using a negligible amount of the heliox mixture. How much heating of the water around the scuba tank results from the change in temperature of the tank?

**Q9: **

A sample of neon gas at a temperature of is put into a steel container of mass 52.7 g that is at a temperature of . The container is modeled as being perfectly rigid and perfectly insulated. The neon and steel reach an equilibrium temperature of . Determine the mass of the sample of neon. Use a value of 20.2 g/mol for the molar mass of neon and use a value of for the specific heat capacity of steel.

**Q10: **

A sealed, perfectly insulated container contains 0.721 mol of air at and a copper stirring bar of mass 42.0 g. The stirring bar is magnetically accelerated until it has 74.2 J of kinetic energy, and then decelerated to rest by drag forces due to the air. What is the equilibrium temperature of the bar and the air after the bar comes to rest?

**Q11: **

A steel container of mass 135 g contains 24.0 g of ammonia. The container and gas are in equilibrium at a temperature of . Determine how much energy must be lost from the container for it to reach a temperature of . Ignore the change in volume of the steel. Use a value of for the specific heat capacity of steel, use a value of for the specific heat capacity of ammonia, and use a value of 17.0 g/mol for the molar mass of ammonia.

- A J
- B J
- C J
- D J
- E J

**Q12: **

Heliox, a mixture of helium and oxygen, is sometimes given to hospital patients who have trouble breathing, because the low mass of helium makes it easier to breathe than air. Suppose helium at is mixed with oxygen at to make a mixture that is helium by mole. What is the final temperature? Ignore any heat flow to or from the surroundings, and assume the final volume is the sum of the initial volumes.