Question 1

In an isochoric process, the internal (thermal) energy of an ideal gas decreases by 50 J. How much heat is exchanged with the gas during this process?

Accepted Answer

In an isochoric process, the volume of the gas remains constant, and no work is done by or on the gas. Therefore, any change in the internal energy of the gas is due entirely to heat exchange. If the internal energy decreases by 50 J, it means that the gas has released 50 J of heat to its surroundings. Hence, the heat exchanged with the gas is -50 J, indicating heat is lost by the gas.

Question 2

The figure shows the pV diagram for a certain thermodynamic process. In this process,
1500 J of heat flows into a system, and at the same time the system expands against a constant external pressure of  If the volume of the system increases from  to  calculate the change in internal (thermal) energy of the system. If the internal (thermal) energy change is nonzero, be sure to indicate whether this energy change is positive or negative.

Accepted Answer

The answer of The figure shows the pV diagram for...

Question 3

A fixed amount of ideal gas goes through a process abc. In state a, the temperature of the gas is 152°C, its pressure is 1.25 atm, and it occupies a volume of 0.250 m³. It then undergoes an isothermal expansion to state b that doubles its volume, followed by an isobaric compression back to its original volume at state c. (Hint: First show this process on a pV diagram.) The ideal gas constant is , and 1.00 atm = 1.01 × 10⁵ Pa. (a) How many moles does this gas contain? (b) What is the change in the internal energy of the gas between states a and b? (c) What is the net work done on (or by) this gas during the entire process? (d) What is the temperature of the gas in state c?

Accepted Answer

The answer of A fixed amount of ideal gas goes...

Question 4

An ideal gas is allowed to expand slowly at constant temperature to twice its original volume. During the expansion, the gas absorbs 200 kJ of heat.
(a) What is the change in the internal (thermal) energy of the gas during the expansion?
(b) How much work does the gas do during the expansion?

Accepted Answer

The answer of An ideal gas is allowed to expand...

Question 5

A system has a heat source supplying heat to an ideal gas at a rate of 187.0 W and the gas is doing work at a rate of 130.9 W. At what rate is the internal (thermal) energy of the gas changing?

Accepted Answer

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Therefore, the rate of change in internal energy is given by:

ΔU/Δt = Q - W

where ΔU/Δt is the rate of change in internal energy, Q is the rate of heat added to the system, and W is the rate of work done by the system. Plugging in the given values:

ΔU/Δt = 187.0 W - 130.9 W 
ΔU/Δt = 56.1 W

Therefore, the answer is A) 56.1 W.

Question 6

A cylinder contains 1.2 moles of ideal gas, initially at a temperature of 116°C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of on the gas. The gas is cooled until its temperature has decreased to 27°C. For the gas C_V = 11.65 J/mol · K, and the ideal gas constant R = 8.314 J/mol ∙ K. (a) Find the work done by (or on) the gas during this process. Is the work done by or on the gas? (b) What is the change in the internal (thermal) energy of the gas during this process? (c) How much heat is transferred to (or from) the gas during this process? Does this heat flow into or out of the gas?

Accepted Answer

The answer of A cylinder contains 1.2 moles of ideal...

Question 7

The pV diagram shown is for 7.50 moles of an ideal diatomic gas taken through a cycle from a to b to c. The ideal gas constant is R = 8.314 J/mol ∙ K.  (a) What is the highest temperature reached by the gas during the cycle?
(b) What net work does the gas do during the cycle?
(c) How much heat is exchanged with the gas during part bc of the cycle? Does it enter or leave the gas?
(d) What is the change in the internal (thermal) energy of the gas during part bc of the cycle?
(e) What is the change in the internal (thermal) energy of the gas during the entire cycle?

Accepted Answer

The answer of The pV diagram shown is for 7.50...

Question 8

A cylinder contains 24.0 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.63 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol · K and the ideal gas constant is R = 8.314 J/mol ∙ K. The change in the internal (thermal) energy of the gas is closest to

Accepted Answer

The answer of A cylinder contains 24.0 moles of an...

Question 9

During an adiabatic process, 20 moles of a monatomic ideal gas undergo a temperature change from 450 K to 320 K starting from an initial pressure is 400 kPa. The ideal gas constant is R = 8.314 J/mol ∙ K.
(a) What is the final volume of the gas?
(b) How much heat does the gas exchange during this process?
(c) What is the change in the internal (thermal) energy of the gas during this process?

Accepted Answer

The answer of During an adiabatic process, 20 moles of...

Question 10

In a thermodynamic process involving 7.8 moles of an ideal gas, the gas is at an initial temperature of 24°C and has an initial volume of 0.040 m³. The gas expands adiabatically to a volume of 0.080 m³. For this gas, C_V = 12.27 J/mol · K, and the ideal gas constant is R = 8.314 J/mol ∙ K. Calculate the work done by the gas during this expansion.

Accepted Answer

The answer of In a thermodynamic process involving 7.8 moles...

Question 11

In an isochoric process, the internal (thermal) energy of an ideal gas decreases by 50 J. How much work does the gas do during this process?

Accepted Answer

In an isochoric process, the volume is kept constant. This means that no work is done by or on the gas, as work is defined as force times displacement, and there is no displacement in this case. Therefore, the work done by the gas is 0 J. The decrease in internal energy is solely due to heat leaving the gas.

Question 12

An ideal gas initially at 300 K and occupying a volume of 20 L is adiabatically compressed. If its final temperature is 400 K and γ = 1.30, what is its final volume?

Accepted Answer

For an adiabatic process, the relation between temperature and volume is given by $T_1V_1^{\gamma-1} = T_2V_2^{\gamma-1}$, where $T_1$ and $T_2$ are the initial and final temperatures, $V_1$ and $V_2$ are the initial and final volumes, and $\gamma$ is the heat capacity ratio. Rearranging for $V_2$, and substituting the given values ($T_1 = 300 K$, $T_2 = 400 K$, $V_1 = 20 L$, $\gamma = 1.30$), we can solve for $V_2$, which results in approximately 7.7 L.

Question 13

The gas in a perfectly insulated system does work at a rate of  At what rate is the internal (thermal) energy of the gas changing?

Accepted Answer

The answer of The gas in a perfectly insulated system...

Question 14

An ideal gas with γ = 1.30 occupies 7.0 L at 300 K and 200 kPa pressure. It is compressed adiabatically to 1/7 of its original volume, then cooled at constant volume to 300 K, and finally allowed to expand isothermally to 7.0 L. How much work does the gas do during this process? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.

Accepted Answer

The answer of An ideal gas with γ = 1.30...

Question 15

A cylinder contains 23 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.43 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol · K and the ideal gas constant is R = 8.314 J/mol ∙ K. The heat absorbed by the gas is closest to

Accepted Answer

The answer of A cylinder contains 23 moles of an...

Question 16

A container with rigid walls is filled with 4 mol of air with C_V = 2.5R. How much does the internal (thermal) energy change if the temperature of the air rises from 16°C to 437°C? The ideal gas constant is R = 8.314 J/mol ∙ K.

Accepted Answer

The answer of A container with rigid walls is filled...

Quiz 19: Work, Heat, and the First Law of Thermodynamics

In an isochoric process, the internal (thermal) energy of an ideal gas decreases by 50 J. How much heat is exchanged with the gas during this process?

An ideal gas is allowed to expand slowly at constant temperature to twice its original volume. During the expansion, the gas absorbs 200 kJ of heat. (a) What is the change in the internal (thermal) energy of the gas during the expansion? (b) How much work does the gas do during the expansion?

A system has a heat source supplying heat to an ideal gas at a rate of 187.0 W and the gas is doing work at a rate of 130.9 W. At what rate is the internal (thermal) energy of the gas changing?

In an isochoric process, the internal (thermal) energy of an ideal gas decreases by 50 J. How much work does the gas do during this process?

An ideal gas initially at 300 K and occupying a volume of 20 L is adiabatically compressed. If its final temperature is 400 K and γ = 1.30, what is its final volume?

The gas in a perfectly insulated system does work at a rate of At what rate is the internal (thermal) energy of the gas changing?

A container with rigid walls is filled with 4 mol of air with CV = 2.5R. How much does the internal (thermal) energy change if the temperature of the air rises from 16°C to 437°C? The ideal gas constant is R = 8.314 J/mol ∙ K.

A container with rigid walls is filled with 4 mol of air with C_V = 2.5R. How much does the internal (thermal) energy change if the temperature of the air rises from 16°C to 437°C? The ideal gas constant is R = 8.314 J/mol ∙ K.