Question 1

Which one of the following statements best describes the operation of a heat engine?

Accepted Answer

A heat engine operates by using input heat to perform work, and then rejecting excess heat to a lower temperature reservoir. This is the basis of the Carnot cycle and is the most common type of heat engine used in industry and transportation. Option B is incorrect because it violates the first law of thermodynamics, which states that energy cannot be created or destroyed, only converted from one form to another. Option C is incorrect because it describes a heat pump, which takes heat from a cold reservoir and transfers it to a hot reservoir. Option D is also incorrect because it describes a heat pump in reverse. Finally, option E is incorrect because it is a generalized statement about entropy, but does not describe the specific operation of a heat engine.

Question 2

In a reversible heat engine, one mole of an ideal gas is carried through a circular cycle beginning and ending at point A as shown in the figure. Which one of the following statements concerning this system is false?

Accepted Answer

The answer of In a reversible heat engine, one mole...

Question 3

Which one of the following statements is true concerning the ratio of the molar heat capacities C_p/C_vfor an ideal gas?

Accepted Answer

For an ideal gas, the ratio of molar heat capacities C_p/C_v (also known as the heat capacity ratio or gamma, γ) is always greater than 1. This is because C_p includes the work done by the system during expansion at constant pressure, in addition to the heat required to raise the temperature, whereas C_v only includes the heat required to raise the temperature at constant volume.

Question 4

A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 10S1U1P15S1S1P0 J of heat is removed from the hot reservoir and 5.0 × 10S1U1P14S1S1P0 J of work is performed.
-What is the actual efficiency of this engine?

Accepted Answer

The answer of A heat engine operates between a hot...

Question 5

Two moles of an ideal gas have an initial Kelvin temperature Ti and absolute pressure Pi. The gas undergoes a reversible isothermal compression from an initial volume Vi to a final volume 0.5Vi.
-What is the change in entropy of the sample?

Accepted Answer

The answer of Two moles of an ideal gas have...

Question 6

Determine the quantity of heat added to 2.8 moles of the ideal gas argon if the temperature increases from 75 °C to 225 °C during an isobaric process. Note: The molar specific heats of argon are C_V = 3.0 cal/K·mol and C_P = 5.0 cal/K·mol.

Accepted Answer

We can use the formula for the heat transferred during an isobaric process:

Q = nCpΔT

Where Q is the heat transferred, n is the number of moles, Cp is the molar specific heat at constant pressure, and ΔT is the change in temperature.

Plugging in the given values and using the molar specific heat at constant pressure, we get:

Q = (2.8 mol) (5.0 cal/K·mol) (225 °C - 75 °C)
Q = 2,100 cal

Therefore, the answer is B.

Question 7

A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 10S1U1P15S1S1P0 J of heat is removed from the hot reservoir and 5.0 × 10S1U1P14S1S1P0 J of work is performed.
-Determine the Carnot efficiency of this engine.

Accepted Answer

The Carnot efficiency of a heat engine is given by
η = 1 - T_c/T_h
where T_c is the temperature of the cold reservoir and T_h is the temperature of the hot reservoir.

In this case, T_h = 1500 K and T_c = 500 K. Thus, the Carnot efficiency is
η = 1 - T_c/T_h = 1 - 500/1500 = 0.67

Therefore, the best choice is D.

Question 8

What change in temperature occurs when 1600 J of heat are removed from 3.0 moles of monatomic gas under constant pressure?

Accepted Answer

The answer of What change in temperature occurs when 1600...

Question 9

A Carnot heat engine is to be designed with an efficiency of 81%. If the low temperature reservoir is 25 °C, what is the temperature of the "hot" reservoir?

Accepted Answer

The efficiency of a Carnot engine is given by:

η = 1 - T_low / T_high

where T_low is the temperature of the low temperature reservoir, and T_high is the temperature of the high temperature reservoir.

We know that the efficiency is 81%, so we can write:

0.81 = 1 - 298 / T_high

Solving for T_high, we get:

T_high = 1 / (1 - 0.81) * 298 = 1574 K = 1300 °C

Therefore, the temperature of the hot reservoir is 1300 °C. The answer is (D).

Question 10

Two moles of an ideal gas have an initial Kelvin temperature Ti and absolute pressure Pi. The gas undergoes a reversible isothermal compression from an initial volume Vi to a final volume 0.5Vi.
-How much heat is exchanged with the environment? If heat is exchanged, is it absorbed or released?

Accepted Answer

Since the gas undergoes a reversible isothermal process, the internal energy of the gas remains constant. Therefore, the heat exchanged with the environment is given by Q = W, where W is the work done on the gas during the compression. Using the formula for the work done during an isothermal process, we have W = nRTi ln(Vi/Vf), where Vf = 0.5Vi. Substituting the values given in the answer choices, we see that only choice A gives the correct expression for Q. The negative sign in front of the expression indicates that the heat is released by the gas to the environment.

Question 11

A gasoline engine with an efficiency of 0.40 generates 1800 W of power. If a liter of gasoline has an energy content of 3.7 × 10⁷ J, how many liters of gasoline does the engine consume each hour?

Accepted Answer

The answer of A gasoline engine with an efficiency of...

Question 12

A Carnot engine has a heat input of 3700 J and heat exhaust of 1400 J. What is the ratio of the Kelvin temperature of the hot reservoir to that of the cold reservoir, T_H/T_C?

Accepted Answer

The efficiency of a Carnot engine is given by 1 - (Q_c/Q_h), where Q_c is the heat exhaust and Q_h is the heat input. The efficiency is also equal to 1 - (T_c/T_h). Solving for T_h/T_c gives (Q_h/Q_c), which is 3700/1400 = 2.64, approximately 2.6.

Question 13

Two engines are identical except that engine A is two years old and engine B is new. If engine A does 15% less work than engine B under identical operating conditions, what is the ratio of the efficiencies of the two engines, e_A/e_B?

Accepted Answer

Let the work done by engine B be W. Then the work done by engine A is 0.85W (since A does 15% less work than B). The efficiency of an engine is defined as the ratio of output work to input energy. Since the two engines are identical except for their age, we can assume that they have the same input energy. Therefore, the ratio of their efficiencies is equal to the ratio of their output work. That is, e_A/e_B = (0.85W)/W = 0.85.

Question 14

An engine is used to lift a 2700-kg truck to a height of 3.0 m at constant speed. In the lifting process, the engine received 4.18 × 10⁵ J of heat from the fuel burned in its interior. What is the efficiency of the engine?

Accepted Answer

The efficiency of the engine is given by the ratio of the work done by the engine to the heat received by the engine. In this case, the work done by the engine is equal to the potential energy gained by the truck, which is mgh = (2700 kg)(9.8 m/s^2)(3.0 m) = 79,860 J. The heat received by the engine is 4.18 × 10^5 J. Therefore, the efficiency of the engine is 79,860 J / 4.18 × 10^5 J = 0.19.

Question 15

A heat engine operates in a Carnot cycle between reservoirs of temperatures 1000 K and 400 K. It is found to discharge 20 J of heat per cycle to the cold reservoir. What is the work output per cycle?

Accepted Answer

In a Carnot cycle, the work output per cycle is given by the difference in the heat absorbed from the hot reservoir and the heat discharged to the cold reservoir, which is:
Work output = Q_hot - Q_cold
where Q_hot is the heat absorbed from the hot reservoir and Q_cold is the heat discharged to the cold reservoir.
In this case, we are given that the heat discharged to the cold reservoir is 20 J per cycle. To find the heat absorbed from the hot reservoir, we can use the Carnot efficiency formula:
Efficiency = 1 - T_cold / T_hot
where T_cold and T_hot are the temperatures of the cold and hot reservoirs, respectively.
Plugging in the values given, we get:
Efficiency = 1 - 400/1000 = 0.6
Thus, the heat absorbed from the hot reservoir is:
Q_hot = Efficiency * Input heat = 0.6 * Output heat
where Input heat is the heat absorbed from the hot reservoir and Output heat is the total heat absorbed from the hot reservoir and the work output per cycle.
Simplifying, we get:
Q_hot = 3/5 * (Q_hot + Work output)
2Q_hot/5 = 3/5 * Work output
Work output = 2/3 * Q_hot = 2/3 * (Q_hot - Q_cold)
Substituting the given values, we get:
Work output = 2/3 * (Q_hot - Q_cold) = 2/3 * (100 J - 20 J) = 60/3 = 20 J.

Question 16

Under which one of the following conditions would a Carnot heat engine be 100% efficient?

Accepted Answer

A Carnot heat engine is 100% efficient when the temperature of the heat source is infinite and the temperature of the heat sink is zero. Discharging heat at 0 K satisfies the condition of having a heat sink at absolute zero temperature, thus making the engine 100% efficient.

Question 17

The ratio of the molar specific heat capacity at constant pressure to that at constant volume, $\gamma$, for diatomic hydrogen gas is 7/5. In an adiabatic compression, the gas, originally at atmospheric pressure, is compressed from an original volume of 0.30 m³ to 0.10 m³. What is the final pressure of the gas?

Accepted Answer

In an adiabatic process, $ P_1 V_1^\gamma = P_2 V_2^\gamma $. Given $ \gamma = 7/5 $, $ P_1 = 1.0 \times 10^5 $ Pa, $ V_1 = 0.30 $ m³, and $ V_2 = 0.10 $ m³, solve for $ P_2 $: $ P_2 = P_1 (V_1/V_2)^\gamma = 1.0 \times 10^5 \times (0.30/0.10)^{7/5} = 4.7 \times 10^5 $ Pa.

Question 18

What is the maximum possible efficiency of an engine operating between the boiling and freezing points of water at sea level?

Accepted Answer

The maximum possible efficiency of an engine is given by the Carnot efficiency, which is 1 - (Tc/Th), where Tc is the cold reservoir temperature and Th is the hot reservoir temperature, both in Kelvin. The boiling point of water is 373K and the freezing point is 273K. Thus, the maximum efficiency = 1 - (273/373) = 0.27 or 27%.

Question 19

Which one of the following statements is not a consequence of the second law of thermodynamics?

Accepted Answer

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. A real refrigerator operates through irreversible processes, causing an increase in the total entropy of the universe, contrary to what option E suggests.

Question 20

A Carnot engine operates between hot and cold reservoirs with temperatures 527 °C and -73.0 °C, respectively. If the engine performs 1000.0 J of work per cycle, how much heat is extracted per cycle from the hot reservoir?

Accepted Answer

The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_c}{T_h}$, where $T_c$ and $T_h$ are the temperatures of the cold and hot reservoirs, respectively, in Kelvin. To convert the given temperatures to Kelvin, add 273.15 to each: $T_h = 527 + 273.15 = 800.15 K$ and $T_c = -73 + 273.15 = 200.15 K$. Thus, $\eta = 1 - \frac{200.15}{800.15}$. The work done (W) is related to the heat extracted from the hot reservoir (Q_h) by the efficiency: $W = \eta \cdot Q_h$. Rearranging for $Q_h$, we get $Q_h = \frac{W}{\eta}$. Substituting the values, we find $Q_h = \frac{1000}{1 - \frac{200.15}{800.15}}$, which calculates to approximately 1333 J.

Quiz 15: Thermodynamics

Which one of the following statements best describes the operation of a heat engine?

In a reversible heat engine, one mole of an ideal gas is carried through a circular cycle beginning and ending at point A as shown in the figure. Which one of the following statements concerning this system is false?

Which one of the following statements is true concerning the ratio of the molar heat capacities C_p/C_vfor an ideal gas?

A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 10⁵ J of heat is removed from the hot reservoir and 5.0 × 10⁴ J of work is performed. -What is the actual efficiency of this engine?

Two moles of an ideal gas have an initial Kelvin temperature Ti and absolute pressure Pi. The gas undergoes a reversible isothermal compression from an initial volume Vi to a final volume 0.5Vi. -What is the change in entropy of the sample?

Determine the quantity of heat added to 2.8 moles of the ideal gas argon if the temperature increases from 75 °C to 225 °C during an isobaric process. Note: The molar specific heats of argon are C_V = 3.0 cal/K·mol and C_P = 5.0 cal/K·mol.

A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 10⁵ J of heat is removed from the hot reservoir and 5.0 × 10⁴ J of work is performed. -Determine the Carnot efficiency of this engine.

What change in temperature occurs when 1600 J of heat are removed from 3.0 moles of monatomic gas under constant pressure?

A Carnot heat engine is to be designed with an efficiency of 81%. If the low temperature reservoir is 25 °C, what is the temperature of the "hot" reservoir?

Two moles of an ideal gas have an initial Kelvin temperature Ti and absolute pressure Pi. The gas undergoes a reversible isothermal compression from an initial volume Vi to a final volume 0.5Vi. -How much heat is exchanged with the environment? If heat is exchanged, is it absorbed or released?

A gasoline engine with an efficiency of 0.40 generates 1800 W of power. If a liter of gasoline has an energy content of 3.7 × 10⁷ J, how many liters of gasoline does the engine consume each hour?

A Carnot engine has a heat input of 3700 J and heat exhaust of 1400 J. What is the ratio of the Kelvin temperature of the hot reservoir to that of the cold reservoir, T_H/T_C?

Two engines are identical except that engine A is two years old and engine B is new. If engine A does 15% less work than engine B under identical operating conditions, what is the ratio of the efficiencies of the two engines, e_A/e_B?

An engine is used to lift a 2700-kg truck to a height of 3.0 m at constant speed. In the lifting process, the engine received 4.18 × 10⁵ J of heat from the fuel burned in its interior. What is the efficiency of the engine?

A heat engine operates in a Carnot cycle between reservoirs of temperatures 1000 K and 400 K. It is found to discharge 20 J of heat per cycle to the cold reservoir. What is the work output per cycle?

Under which one of the following conditions would a Carnot heat engine be 100% efficient?

What is the maximum possible efficiency of an engine operating between the boiling and freezing points of water at sea level?

Which one of the following statements is not a consequence of the second law of thermodynamics?

A Carnot engine operates between hot and cold reservoirs with temperatures 527 °C and -73.0 °C, respectively. If the engine performs 1000.0 J of work per cycle, how much heat is extracted per cycle from the hot reservoir?

Quiz 15: Thermodynamics

Which one of the following statements best describes the operation of a heat engine?

In a reversible heat engine, one mole of an ideal gas is carried through a circular cycle beginning and ending at point A as shown in the figure. Which one of the following statements concerning this system is false?

Which one of the following statements is true concerning the ratio of the molar heat capacities Cp/Cv for an ideal gas?

A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 105 J of heat is removed from the hot reservoir and 5.0 × 104 J of work is performed. -What is the actual efficiency of this engine?

Two moles of an ideal gas have an initial Kelvin temperature Ti and absolute pressure Pi. The gas undergoes a reversible isothermal compression from an initial volume Vi to a final volume 0.5Vi. -What is the change in entropy of the sample?

Determine the quantity of heat added to 2.8 moles of the ideal gas argon if the temperature increases from 75 °C to 225 °C during an isobaric process. Note: The molar specific heats of argon are CV = 3.0 cal/K·mol and CP = 5.0 cal/K·mol.

A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 105 J of heat is removed from the hot reservoir and 5.0 × 104 J of work is performed. -Determine the Carnot efficiency of this engine.

What change in temperature occurs when 1600 J of heat are removed from 3.0 moles of monatomic gas under constant pressure?

A Carnot heat engine is to be designed with an efficiency of 81%. If the low temperature reservoir is 25 °C, what is the temperature of the "hot" reservoir?

Two moles of an ideal gas have an initial Kelvin temperature Ti and absolute pressure Pi. The gas undergoes a reversible isothermal compression from an initial volume Vi to a final volume 0.5Vi. -How much heat is exchanged with the environment? If heat is exchanged, is it absorbed or released?

A gasoline engine with an efficiency of 0.40 generates 1800 W of power. If a liter of gasoline has an energy content of 3.7 × 107 J, how many liters of gasoline does the engine consume each hour?

A Carnot engine has a heat input of 3700 J and heat exhaust of 1400 J. What is the ratio of the Kelvin temperature of the hot reservoir to that of the cold reservoir, TH/TC?

Two engines are identical except that engine A is two years old and engine B is new. If engine A does 15% less work than engine B under identical operating conditions, what is the ratio of the efficiencies of the two engines, eA/eB?

An engine is used to lift a 2700-kg truck to a height of 3.0 m at constant speed. In the lifting process, the engine received 4.18 × 105 J of heat from the fuel burned in its interior. What is the efficiency of the engine?

A heat engine operates in a Carnot cycle between reservoirs of temperatures 1000 K and 400 K. It is found to discharge 20 J of heat per cycle to the cold reservoir. What is the work output per cycle?

Under which one of the following conditions would a Carnot heat engine be 100% efficient?

What is the maximum possible efficiency of an engine operating between the boiling and freezing points of water at sea level?

Which one of the following statements is not a consequence of the second law of thermodynamics?

A Carnot engine operates between hot and cold reservoirs with temperatures 527 °C and -73.0 °C, respectively. If the engine performs 1000.0 J of work per cycle, how much heat is extracted per cycle from the hot reservoir?

Which one of the following statements is true concerning the ratio of the molar heat capacities C_p/C_vfor an ideal gas?

A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 10⁵ J of heat is removed from the hot reservoir and 5.0 × 10⁴ J of work is performed. -What is the actual efficiency of this engine?

Determine the quantity of heat added to 2.8 moles of the ideal gas argon if the temperature increases from 75 °C to 225 °C during an isobaric process. Note: The molar specific heats of argon are C_V = 3.0 cal/K·mol and C_P = 5.0 cal/K·mol.

A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 × 10⁵ J of heat is removed from the hot reservoir and 5.0 × 10⁴ J of work is performed. -Determine the Carnot efficiency of this engine.

A gasoline engine with an efficiency of 0.40 generates 1800 W of power. If a liter of gasoline has an energy content of 3.7 × 10⁷ J, how many liters of gasoline does the engine consume each hour?

A Carnot engine has a heat input of 3700 J and heat exhaust of 1400 J. What is the ratio of the Kelvin temperature of the hot reservoir to that of the cold reservoir, T_H/T_C?

Two engines are identical except that engine A is two years old and engine B is new. If engine A does 15% less work than engine B under identical operating conditions, what is the ratio of the efficiencies of the two engines, e_A/e_B?

An engine is used to lift a 2700-kg truck to a height of 3.0 m at constant speed. In the lifting process, the engine received 4.18 × 10⁵ J of heat from the fuel burned in its interior. What is the efficiency of the engine?