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In this lesson, we will learn how to relate changes of a gas’s bulk properties to its specific heat capacity and so define the first law of thermodynamics.

Q1:

When 400 J of heat are slowly added to 10 mol of an ideal monatomic gas, its temperature rises by 1 0 ∘ C . What is the work done on the gas?

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 3 . 0 × 1 0 2 K. The temperature of each gas is increased by 1 0 ∘ C when they are heated.

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

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

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

Q3:

A helium-filled toy balloon has a gauge pressure of 0.200 atm and a volume of 10.0 L. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?

The specific heat ratio for helium is 1.667.

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 1 2 ∘ C , 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 2 8 ∘ C and a pressure of 1 . 4 4 × 1 0 5 Pa. A block of ice of mass 1.35 kg that is at a temperature of 0 ∘ C is placed in the room. What is the equilibrium temperature of the ice and air? Use a value of 4 1 8 4 / ⋅ J k g C ∘ 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 ( N O 2 ) 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 − 8 8 ∘ C is mixed with 4.0 mol of air (assumed to be diatomic) at a temperature of 3 0 ∘ C . What is the final temperature of the mixture? Use a value of 3 0 . 4 / ⋅ J m o l C ∘ for the specific heat capacity of N O 2 at 2 5 ∘ C .

Q7:

Professional divers sometimes use heliox, which is a mixture by mole of 7 9 % helium and 2 1 % oxygen. A perfectly rigid scuba tank with a volume of 15 L contains heliox at an absolute pressure of 2 . 4 × 1 0 7 Pa and at a temperature of 3 3 ∘ C .

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 2 7 ∘ C 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?

Q8:

2.50 mol of air and 2.50 mol of argon are each heated at constant volume, raising their temperatures from 2 3 . 0 ∘ C to 3 5 . 0 ∘ C .

How much energy is transferred to the air? Model the air as being diatomic.

How much energy is transferred to the argon?

Q9:

A sample of neon gas at a temperature of 2 3 . 0 ∘ C is put into a steel container of mass 52.7 g that is at a temperature of − 4 2 . 3 ∘ C . The container is modeled as being perfectly rigid and perfectly insulated. The neon and steel reach an equilibrium temperature of − 2 5 . 4 ∘ C . 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 4 5 2 / ⋅ J k g C ∘ for the specific heat capacity of steel.

Q10:

A sealed, perfectly insulated container contains 0.721 mol of air at 2 3 . 0 ∘ C 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 1 2 . 0 ∘ C . Determine how much energy must be lost from the container for it to reach a temperature of − 2 0 . 0 ∘ C . Ignore the change in volume of the steel. Use a value of 4 5 2 / ⋅ J k g C ∘ for the specific heat capacity of steel, use a value of 2 1 9 0 / ⋅ J k g C ∘ for the specific heat capacity of ammonia, and use a value of 17.0 g/mol for the molar mass of ammonia.

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 2 5 . 0 ∘ C is mixed with oxygen at 3 5 . 0 ∘ C to make a mixture that is 7 0 . 0 % 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.

Q13:

An ideal gas has a molecular mass of 10 g/mol and a specific internal energy of 300 kJ/kg when its temperature is 373 K. What is the specific enthalpy of this gas?

Q14:

According to the first law of thermodynamics, what cannot be created or destroyed?

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