Question 1

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 heat added during an isobaric process: 
Q = nCpΔT 
where Q is the heat added, n is the number of moles, Cp is the molar specific heat at constant pressure, and ΔT is the change in temperature. 
Substituting the given values: 
Q = (2.8 mol)(5.0 cal/K·mol)(225 °C - 75 °C) 
Q = 2100 cal 
Therefore, the answer is B) 2100 cal.

Question 2

15-5
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 is given by:
η_carnot = 1 - T_cold / T_hot
where T_hot and T_cold are the temperatures of the hot and cold reservoirs, respectively.

Plugging in the values, we get:
η_carnot = 1 - 500 K / 1500 K
η_carnot = 1 - 1/3
η_carnot = 2/3 
η_carnot = 0.67

Therefore, the best choice is (D) with the Carnot efficiency of 0.67.

Question 3

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 4

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.

Question 5

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 6

15-4
Two moles of an ideal gas have an initial Kelvin temperature TS1U1B1i S1U1B0and absolute pressure PS1U1B1iS1U1B0.The gas undergoes a reversible isothermal compression from an initial volume VS1U1B1iS1U1B0 to a final volume 0.5VS1U1B1iS1U1B0.
-What is the change in entropy of the sample?

Accepted Answer

The answer of 15-4
Two moles of an ideal gas have...

Question 7

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 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 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 power output of the gasoline engine is:

P = 1800 W

The efficiency of the engine is:

η = 0.40

The energy content of gasoline is:

E = 3.7 × 10^10 J/L

Let V be the volume of gasoline consumed by the engine in one hour. The amount of energy generated by the engine in one hour is:

P × 3600 s = V × E × η

Substituting the given values, we get:

1800 × 3600 = V × 3.7 × 10^10 × 0.40

Solving for V, we get:

V = 0.44 L/hour

Therefore, the engine consumes 0.44 liters of gasoline each hour. The answer is (B).

Question 10

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

The answer of Which one of the following statements is...

Question 11

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 answer of A Carnot engine has a heat input...

Question 12

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

Accepted Answer

A Carnot heat engine is 100% efficient only when the engine discharges heat at 0 K because then the efficiency of the engine is given by the ratio of the temperatures of the two heat reservoirs, and the temperature of the cold reservoir (0 K) makes the denominator equal to zero, making the efficiency equal to 1 or 100%.

Question 13

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 answer of An engine is used to lift a...

Question 14

15-5
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 15-5
A heat engine operates between a hot...

Question 15

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 16

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's assume that engine B has an efficiency of 100. Then, according to the problem, engine A will have an efficiency of 85 (since it does 15% less work). Therefore, the ratio of the efficiencies of the two engines is: e_A/e_B = 85/100 = 0.85 So, the correct answer is C.

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

The answer of The ratio of the molar specific heat...

Question 18

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

The efficiency of a Carnot engine is given by $ \eta = 1 - \frac{T_c}{T_h} $, where $ T_c $ is the temperature of the cold reservoir and $ T_h $ is the temperature of the hot reservoir. Plugging in the given temperatures (in Kelvin), we get $ \eta = 1 - \frac{400}{1000} = 0.6 $. The work output ($ W $) of the engine can be calculated using the efficiency formula $ \eta = \frac{W}{Q_h} $, where $ Q_h $ is the heat absorbed from the hot reservoir. Since $ Q_c = 20 $ J is discharged to the cold reservoir and $ \eta = 0.6 $, we can use the first law of thermodynamics which states $ Q_h = W + Q_c $. Rearranging the efficiency formula gives $ W = \eta \cdot Q_h $. To find $ Q_h $, we use $ Q_h = \frac{Q_c}{1 - \eta} = \frac{20}{1 - 0.6} = 50 $ J. Therefore, $ W = \eta \cdot Q_h = 0.6 \cdot 50 = 30 $ J.

Question 19

15-4
Two moles of an ideal gas have an initial Kelvin temperature TS1U1B1i S1U1B0and absolute pressure PS1U1B1iS1U1B0.The gas undergoes a reversible isothermal compression from an initial volume VS1U1B1iS1U1B0 to a final volume 0.5VS1U1B1iS1U1B0.
-How much heat is exchanged with the environment? If heat is exchanged, is it absorbed or released?

Accepted Answer

Since the process is reversible and isothermal, we know that the change in internal energy (ΔU) is zero, and therefore, the heat exchanged with the environment (q) equals the work done by the gas (w). Using the formula for reversible isothermal work, we get: w = nRT ln(Vf/Vi) where n = 2 moles, R is the ideal gas constant, and T is the initial temperature in Kelvin. Plugging in the given values and the final volume of 0.5Vi, we get: w = 2 * 8.31 * T_i * ln(0.5) w = -2 * 8.31 * T_i * ln(2) Since the work done by the gas is negative (compression), the heat exchanged with the environment is positive, meaning it is released. Therefore, the correct answer is A.

Question 20

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 rejecting excess heat to a lower temperature reservoir. This process allows for the conversion of thermal energy into mechanical energy, as described by the first law of thermodynamics. Heat engines operate in a cyclic process, meaning that the same steps are repeated over and over again. One example of a heat engine is the internal combustion engine commonly used in automobiles.

Quiz 15: Thermodynamics

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.

15-5 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.

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?

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

15-4 Two moles of an ideal gas have an initial Kelvin temperature T_iand absolute pressure P_i.The gas undergoes a reversible isothermal compression from an initial volume V_i to a final volume 0.5V_i. -What is the change in entropy of the sample?

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?

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

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?

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

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?

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

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?

15-5 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?

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?

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?

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?

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

Quiz 15: Thermodynamics

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.

15-5 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.

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?

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

15-4 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?

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?

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

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?

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

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?

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

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?

15-5 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?

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?

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?

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?

15-4 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?

Which one of the following statements best describes the operation of a heat 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.

15-5 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.

15-4 Two moles of an ideal gas have an initial Kelvin temperature T_iand absolute pressure P_i.The gas undergoes a reversible isothermal compression from an initial volume V_i to a final volume 0.5V_i. -What is the change in entropy of the sample?

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?

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

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?

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?

15-5 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 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?