Question 1

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

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Question 2

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.

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Question 3

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 (constant volume) process, the work done by the gas is given by the equation W = 0, since the volume is constant and there is no change in the boundary work. Therefore, the work done by the gas is 0 J. The decrease in internal energy of the gas is solely due to the heat energy leaving the system (Q), as given by the First Law of Thermodynamics: ΔU = Q - W, where W=0.

Question 4

If we use 67 W of power to heat 148 g of water, how long will it take to raise the temperature of the water from 15°C to 25°C? The specific heat of water is 4190 J/kg•K.

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Question 5

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 9.00 x 10⁴ Pa. If the volume of the system increases from 0.020 m³ to 0.050 m³, 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.

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Question 6

A 648-g empty iron kettle is put on a stove. How much heat. in joules. must it absorb to raise its temperature from 15.0°C to 37.0°C? (The specific heat for iron is 113 cal/kg•C°, 1 cal = 4.190 J)

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Question 7

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 8

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 6.4 x 10⁵ Pa on the gas. The gas is cooled until its temperature has decreased to 27°C For the gas and the ideal gas constant (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?

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Question 9

The gas in a perfectly insulated system does work at a rate of 13 W. At what rate is the internal (thermal) energy of the gas changing?

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Question 10

It is necessary to determine the specific heat of an unknown object. The mass of the object is measured to be 199.0 g. It is determined experimentally that it takes 16.0 J to raise the temperature 10.0°C. Find the specific heat of the object.

Accepted Answer

The specific heat (c) can be found using the formula:
c = Q/(mΔT)
where Q is the amount of heat energy transferred, m is the mass of the object, and ΔT is the change in temperature.

Plugging in the values given:
c = 16.0 J/(0.199 kg × 10.0°C)
c = 8.04 J/kg ∙ K

Therefore, the specific heat of the object is 8.04 J/kg ∙ K, which corresponds to choice A.

Question 11

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 8.314 J/mol ∙ K, 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?

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Question 12

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?

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Question 13

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

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Question 14

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 15

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 16

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?

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Question 17

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.

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Question 18

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.

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Question 19

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?

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Question 20

During an adiabatic process, an ideal gas does 25 J of work. What is the change in the internal (thermal) energy of the gas during this process?

Accepted Answer

In an adiabatic process, the gas does not exchange heat with the surroundings, so there is no change in the thermal energy of the gas. Therefore, the change in internal energy of the gas is equal to the negative of the work done by the gas. So, the change in internal energy of the gas = -25 J.

Quiz 17: Work, Heat, and the First Law of Thermodynamics