Question 1

A car of mass 2000 kg is traveling at 22.0 m/s on a day when the temperature is 20.0ºC. The driver steps on the brakes and stops the car. By how much does the entropy of the universe increase?

Accepted Answer

The entropy of the universe increases due to the conversion of the car's kinetic energy into heat and its subsequent dissipation into the environment. The change in entropy ($\Delta S$) can be calculated using the formula $\Delta S = \frac{Q}{T}$, where $Q$ is the heat generated (equal to the kinetic energy lost by the car) and $T$ is the absolute temperature in Kelvin.First, convert the temperature from Celsius to Kelvin: $T = 20.0ºC + 273.15 = 293.15 K$.Calculate the kinetic energy ($KE$) lost by the car: $KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 2000 \times (22.0)^2 = 484000 J$ or $484 kJ$.Then, calculate the change in entropy: $\Delta S = \frac{Q}{T} = \frac{484 kJ}{293.15 K} \approx 1.65 kJ/K$.The closest answer is 1.6 kJ/K.

Question 2

What is the entropy change when 4 kg of water at 0S1U1P1$\circ$S1S1P0C is frozen into 4 kg of ice at 0S1U1P1$\circ$S1S1P0C?

Accepted Answer

When water freezes, its molecules become more organized, resulting in a decrease in entropy. The entropy change can be calculated using the formula ΔS = q/T, where q is the heat transferred and T is the temperature. At 0°C, the heat required to freeze 4 kg of water is 4 kg x 333.5 kJ/kg = 1334 kJ. The temperature remains constant during the phase change, so T = 273 K. Thus, ΔS = 1334 kJ / 273 K = 4.89 kJ/K, which is approximately equal to 4.9 kJ/K. Therefore, the best choice is C.

Question 3

What is the maximum possible coefficient of performance of a heat pump that is capable of maintaining the interior of a house at +20ºC when the temperature outside is -40ºC?

Accepted Answer

The answer of What is the maximum possible coefficient of...

Question 4

Two moles of a gas at T = 350 K expand quasistatically and isothermally from an initial volume of 20 L to a final volume of 60 L. The change in entropy of the gas during this expansion is (R = 8.314 J/mol·K)

Accepted Answer

For an isothermal process, we know that $\Delta S_{sys}=-\Delta S_{surr}$, where $S_{sys}$ is the entropy change of the system and $S_{surr}$ is the entropy change of the surroundings. Since the expansion is quasi-static, it is reversible and the surroundings can be assumed to be an infinite reservoir of heat at constant temperature.

The change in entropy of the surroundings is given by $\Delta S_{surr}=-\frac{Q}{T}$, where $Q$ is the heat absorbed by the surroundings. For an isothermal process, $Q=T\Delta S_{sys}$, so we have:

$$\Delta S_{surr}=-\frac{Q}{T}=-\frac{T\Delta S_{sys}}{T}=-\Delta S_{sys}$$

Therefore, $\Delta S_{sys}= \Delta S_{surr} = -\frac{nR}{V}\ln\frac{V_f}{V_i}$, where $n$ is the number of moles of the gas, $V_i$ is the initial volume, and $V_f$ is the final volume.

Plugging in the values, we get:

$$\Delta S_{sys}=-\frac{2\cdot8.314}{20}\ln\frac{60}{20}=18.3	ext{ J/K}$$

Hence, the answer is B).

Question 5

A container has 0.2 mole of O₂ gas and the gas is heated from 0S1U1P1$\circ$S1S1P0C to 100S1U1P1$\circ$S1S1P0C. What is the change in entropy of the gas? (R = 8.314 J/mol·K)

Accepted Answer

First, we need to calculate the initial and final entropy of the gas using the formula: ΔS = nCln(T2/T1) - nRln(V2/V1) where ΔS is the change in entropy, n is the number of moles, C is the molar heat capacity at constant volume, R is the gas constant, T1 and T2 are the initial and final temperatures, and V1 and V2 are the initial and final volumes (assuming constant volume). At constant volume: ΔS = nCvln(T2/T1) - nRln(V2/V1) where Cv is the molar heat capacity at constant volume. Since O₂ gas is a diatomic gas, Cv = (5/2)R. Plugging in the values, we get: ΔS = (0.2 mol)(5/2)(8.314 J/mol·K)ln(100/0) - (0.2 mol)(8.314 J/mol·K)ln(1) ΔS = (2.61 J/K/mol)(ln10) ΔS ≈ 1.82 J/K Therefore, the correct answer is A) 1.82 J/K.

Question 6

When you make ice cubes, the entropy of the water

Accepted Answer

When water freezes to form ice cubes, its molecules become more ordered compared to their arrangement in the liquid state. This increased order means the system's entropy decreases.

Question 7

The change in the entropy of the universe due to an operating Carnot engine

Accepted Answer

The Carnot engine is an idealized reversible engine, meaning that it operates without any friction or energy losses. As a result, the total entropy of the universe remains unchanged, making the answer A, zero.

Question 8

A block of mass m = 0.2 kg slides across a rough horizontal surface with coefficient of kinetic friction $\mu$_k = 0.5. What is the change in entropy after the block has moved a distance of 1 m? The temperature of the block and surrounding is 22S1U1P1$\circ$S1S1P0C.

Accepted Answer

The change in entropy can be calculated using the equation ΔS = -Q/T, where Q is the heat transferred during the process and T is the temperature. In this case, there is no heat transferred, so ΔS = 0, and the answer is E) zero.

Alternatively, the change in entropy can be calculated using the formula ΔS = -mukNln(d2/d1), where N is the normal force, d2 is the final position, and d1 is the initial position. The normal force N can be found using N = mg, and the distance d2 - d1 is 1 m. Plugging in the numbers, we get ΔS = -(0.2 kg)(0.5)(0.2 kg)(9.8 m/s^2)ln(2) = -3.3 J/K, which is closest to choice B). However, this calculation assumes that all the work done by the friction force is converted to heat, which may not be completely true in reality. Hence, the more accurate answer is still E) zero.

Question 9

An ideal heat pump is used to pump head from the outside air at -5ºC to the hot-air supply for the heating fan in a house, which is at 35ºC. How much work is required to pump
1)5 kJ of heat into the house?

Accepted Answer

The ideal heat pump working between temperatures $T_{1}$ and $T_{2}$, where $T_{2}>T_{1}$, has a coefficient of performance (COP) defined by $	ext{COP}=\frac{Q_{1}}{W}$, where $Q_{1}$ is the amount of heat extracted from the low-temperature reservoir and $W$ is the work input. The COP of this heat pump is $	ext{COP}=\frac{T_{2}}{T_{2}-T_{1}}$. Therefore, the heat pump requires 
\begin{align*}
W&=\frac{Q_{1}}{	ext{COP}} \
&=\frac{(5	ext{ kJ})}{\left(\frac{308	ext{ K}}{308	ext{ K}-268	ext{ K}}ight)} \
&=0.195	ext{ kJ}.
\end{align*}

Question 10

Entropy is related to probability. An isolated system moves toward

Accepted Answer

Entropy is a measure of the number of possible microscopic arrangements of a system that result in the same macroscopic state. A state of low order (i.e. high randomness), high probability (i.e. more possible arrangements), and high entropy is most likely for an isolated system.

Question 11

A heat pump needs to supply 20 kW of power to maintain the inside temperature of a house at 25S1U1P1$\circ$S1S1P0C while the outside temperature is 0S1U1P1$\circ$S1S1P0C. What is the power needed for the heat pump?

Accepted Answer

The answer of A heat pump needs to supply 20...

Question 12

What is the maximum possible coefficient of performance of a heat pump that is capable of maintaining the interior of a house at 23ºC when the temperature outside is -30ºC?

Accepted Answer

The answer of What is the maximum possible coefficient of...

Question 13

A heat pump needs to supply 20 kW of power to maintain the inside temperature of a house at 25S1U1P1$\circ$S1S1P0C while the outside temperature is 0S1U1P1$\circ$S1S1P0C. What is the savings in the electric bill per month by using the heat pump instead of direct electrical heating? Assume that the heat pump/direct heating is on for 4 hours per day and 1 kW.hr costs $0.10.

Accepted Answer

To calculate the savings, we first need to determine the energy consumption and cost for both the heat pump and direct electrical heating.For direct electrical heating, the energy required is directly equal to the heat needed. So, for 4 hours per day:Energy required per day = 20 kW * 4 hours = 80 kWhEnergy required per month (assuming 30 days) = 80 kWh/day * 30 days = 2400 kWhCost for direct heating per month = 2400 kWh * $0.10/kWh = $240For the heat pump, we use the Coefficient of Performance (COP) to find its efficiency. The COP for a heat pump is given by:$$COP = \frac{T_{hot}}{T_{hot} - T_{cold}}$$where $T_{hot}$ and $T_{cold}$ are the temperatures inside and outside, respectively, in Kelvin.Converting the temperatures to Kelvin:$$T_{hot} = 25°C + 273.15 = 298.15 K$$$$T_{cold} = 0°C + 273.15 = 273.15 K$$$$COP = \frac{298.15}{298.15 - 273.15} = \frac{298.15}{25} = 11.926$$The effective energy consumption of the heat pump per day is:$$Energy = \frac{Energy required}{COP} = \frac{80 kWh}{11.926} \approx 6.71 kWh$$Energy required per month = 6.71 kWh/day * 30 days = 201.3 kWhCost for heat pump heating per month = 201.3 kWh * $0.10/kWh = $20.13Savings per month = Cost for direct heating - Cost for heat pump heatingSavings = $240 - $20.13 = $219.87Rounding to the nearest whole number, the savings are approximately $220 per month.

Question 14

Three moles of a gas at T = 250 K expand quasi-statically and adiabatically from an initial volume of 30 L to a final volume of 60 L. The change in entropy of the gas during this expansion is (R = 8.314 J/mol·K)

Accepted Answer

In an adiabatic process, there is no heat exchange with the surroundings. The change in entropy for a quasi-static adiabatic process is zero because entropy is a function of heat transfer.

Question 15

A thermodynamic system is taken in equilibrium steps from State I to State II. The quantities by which the process can be characterized are

1  internal energy,
	2  entropy,
	3  temperature,
	4  work, and
	5  heat.

Of these quantities, those that are independent of path are

Accepted Answer

The answer of A thermodynamic system is taken in equilibrium...

Question 16

One mole of an ideal gas undergoes a reversible isothermal expansion from a volume of 1 L to a volume of 2 L. The change in entropy of the gas in terms of the universal gas constant R is

Accepted Answer

For an isothermal process, the change in entropy is given by:
ΔS = nR ln(V2/V1)
where n is the number of moles of the gas, R is the universal gas constant, and V2 and V1 are the final and initial volumes, respectively. Substituting the given values, we have:
ΔS = (1 mol)(R) ln(2/1) = R ln(2)

Question 17

A steam power plant with an efficiency of 65% of the maximum thermodynamic efficiency operates between 250º C and 40ºC. What is the change in the entropy of the universe when this plant does 1.0 kJ of work?

Accepted Answer

The change in the entropy of the universe can be calculated using the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the amount of heat transferred, and T is the temperature at which the heat is transferred. Since the plant does 1.0 kJ of work, the amount of heat transferred is also 1.0 kJ (due to the first law of thermodynamics). The temperature at which heat is transferred is the average temperature of the plant, which can be calculated as (250+40)/2 = 145ºC = 418K. The maximum thermodynamic efficiency for a Carnot cycle operating between these temperatures is given by (250-40)/250 = 0.84, so the actual efficiency of 65% corresponds to a Carnot efficiency of 0.65/0.84 = 0.77. Therefore, the amount of heat absorbed by the plant is Q_in = 0.77*1.0 kJ = 0.77 kJ, and the amount of heat rejected is Q_out = 0.23*1.0 kJ = 0.23 kJ. The entropy change for the plant can be calculated using the equation ΔS_plant = (Q_in/T_in) - (Q_out/T_out) = (0.77 kJ/418K) - (0.23 kJ/313K) = 0.0017 kJ/K. The entropy change for the surroundings can be calculated using the equation ΔS_surroundings = -ΔS_plant = -0.0017 kJ/K. The total entropy change for the universe (plant + surroundings) is ΔS_universe = ΔS_plant + ΔS_surroundings = 0.0017 kJ/K - 0.0017 kJ/K = 0 kJ/K. However, the question asks for the entropy change in Joules per Kelvin (J/K), so we need to convert 0.0017 kJ/K to J/K by multiplying by 1000, which gives ΔS_universe = 1.7 J/K. Therefore, the correct answer is B.

Question 18

Which of the following statements is true of an isolated system consisting of 15 gas molecules?

Accepted Answer

The second law of thermodynamics states that in any spontaneous process, the total entropy of the universe increases. Therefore, the entropy of the gas is not likely to decrease in an isolated system consisting of 15 gas molecules. However, it is possible for the entropy of the gas to remain constant or increase due to random fluctuations in the positions and velocities of the gas molecules.

Question 19

A heat pump with COP = 5 uses electrical energy W to heat a house. How much heat is pumped into the house?

Accepted Answer

The answer of A heat pump with COP = 5...

Question 20

A quantity of heat is removed from a hot reservoir at absolute temperature T and then is added to a cold reservoir at absolute temperature T/2. The cold reservoir experiences an entropy increase S. What is the change in the entropy of the universe?

Accepted Answer

The answer of A quantity of heat is removed from...

Quiz 19: The Second Law of Thermodynamics

A car of mass 2000 kg is traveling at 22.0 m/s on a day when the temperature is 20.0ºC. The driver steps on the brakes and stops the car. By how much does the entropy of the universe increase?

What is the entropy change when 4 kg of water at 0^$\circ$C is frozen into 4 kg of ice at 0^$\circ$C?

What is the maximum possible coefficient of performance of a heat pump that is capable of maintaining the interior of a house at +20ºC when the temperature outside is -40ºC?

Two moles of a gas at T = 350 K expand quasistatically and isothermally from an initial volume of 20 L to a final volume of 60 L. The change in entropy of the gas during this expansion is (R = 8.314 J/mol·K)

A container has 0.2 mole of O₂ gas and the gas is heated from 0^$\circ$C to 100^$\circ$C. What is the change in entropy of the gas? (R = 8.314 J/mol·K)

When you make ice cubes, the entropy of the water

The change in the entropy of the universe due to an operating Carnot engine

A block of mass m = 0.2 kg slides across a rough horizontal surface with coefficient of kinetic friction $\mu$ _k = 0.5. What is the change in entropy after the block has moved a distance of 1 m? The temperature of the block and surrounding is 22^$\circ$C.

An ideal heat pump is used to pump head from the outside air at -5ºC to the hot-air supply for the heating fan in a house, which is at 35ºC. How much work is required to pump 1) 5 kJ of heat into the house?

Entropy is related to probability. An isolated system moves toward

A heat pump needs to supply 20 kW of power to maintain the inside temperature of a house at 25^$\circ$C while the outside temperature is 0^$\circ$C. What is the power needed for the heat pump?

What is the maximum possible coefficient of performance of a heat pump that is capable of maintaining the interior of a house at 23ºC when the temperature outside is -30ºC?

Three moles of a gas at T = 250 K expand quasi-statically and adiabatically from an initial volume of 30 L to a final volume of 60 L. The change in entropy of the gas during this expansion is (R = 8.314 J/mol·K)

A thermodynamic system is taken in equilibrium steps from State I to State II. The quantities by which the process can be characterized are 1 internal energy, 2 entropy, 3 temperature, 4 work, and 5 heat. Of these quantities, those that are independent of path are

One mole of an ideal gas undergoes a reversible isothermal expansion from a volume of 1 L to a volume of 2 L. The change in entropy of the gas in terms of the universal gas constant R is

A steam power plant with an efficiency of 65% of the maximum thermodynamic efficiency operates between 250º C and 40ºC. What is the change in the entropy of the universe when this plant does 1.0 kJ of work?

Which of the following statements is true of an isolated system consisting of 15 gas molecules?

A heat pump with COP = 5 uses electrical energy W to heat a house. How much heat is pumped into the house?

A quantity of heat is removed from a hot reservoir at absolute temperature T and then is added to a cold reservoir at absolute temperature T/2. The cold reservoir experiences an entropy increase S. What is the change in the entropy of the universe?

Quiz 19: The Second Law of Thermodynamics

A car of mass 2000 kg is traveling at 22.0 m/s on a day when the temperature is 20.0ºC. The driver steps on the brakes and stops the car. By how much does the entropy of the universe increase?

What is the entropy change when 4 kg of water at 0 ∘\circ∘ C is frozen into 4 kg of ice at 0 ∘\circ∘ C?

What is the maximum possible coefficient of performance of a heat pump that is capable of maintaining the interior of a house at +20ºC when the temperature outside is -40ºC?

Two moles of a gas at T = 350 K expand quasistatically and isothermally from an initial volume of 20 L to a final volume of 60 L. The change in entropy of the gas during this expansion is (R = 8.314 J/mol·K)

A container has 0.2 mole of O2 gas and the gas is heated from 0 ∘\circ∘ C to 100 ∘\circ∘ C. What is the change in entropy of the gas? (R = 8.314 J/mol·K)

When you make ice cubes, the entropy of the water

The change in the entropy of the universe due to an operating Carnot engine

A block of mass m = 0.2 kg slides across a rough horizontal surface with coefficient of kinetic friction μ\muμ k = 0.5. What is the change in entropy after the block has moved a distance of 1 m? The temperature of the block and surrounding is 22 ∘\circ∘ C.

An ideal heat pump is used to pump head from the outside air at -5ºC to the hot-air supply for the heating fan in a house, which is at 35ºC. How much work is required to pump 1) 5 kJ of heat into the house?

Entropy is related to probability. An isolated system moves toward

A heat pump needs to supply 20 kW of power to maintain the inside temperature of a house at 25 ∘\circ∘ C while the outside temperature is 0 ∘\circ∘ C. What is the power needed for the heat pump?

What is the maximum possible coefficient of performance of a heat pump that is capable of maintaining the interior of a house at 23ºC when the temperature outside is -30ºC?

Three moles of a gas at T = 250 K expand quasi-statically and adiabatically from an initial volume of 30 L to a final volume of 60 L. The change in entropy of the gas during this expansion is (R = 8.314 J/mol·K)

A thermodynamic system is taken in equilibrium steps from State I to State II. The quantities by which the process can be characterized are 1 internal energy, 2 entropy, 3 temperature, 4 work, and 5 heat. Of these quantities, those that are independent of path are

One mole of an ideal gas undergoes a reversible isothermal expansion from a volume of 1 L to a volume of 2 L. The change in entropy of the gas in terms of the universal gas constant R is

A steam power plant with an efficiency of 65% of the maximum thermodynamic efficiency operates between 250º C and 40ºC. What is the change in the entropy of the universe when this plant does 1.0 kJ of work?

Which of the following statements is true of an isolated system consisting of 15 gas molecules?

A heat pump with COP = 5 uses electrical energy W to heat a house. How much heat is pumped into the house?

A quantity of heat is removed from a hot reservoir at absolute temperature T and then is added to a cold reservoir at absolute temperature T/2. The cold reservoir experiences an entropy increase S. What is the change in the entropy of the universe?

What is the entropy change when 4 kg of water at 0^$\circ$C is frozen into 4 kg of ice at 0^$\circ$C?

A container has 0.2 mole of O₂ gas and the gas is heated from 0^$\circ$C to 100^$\circ$C. What is the change in entropy of the gas? (R = 8.314 J/mol·K)

A block of mass m = 0.2 kg slides across a rough horizontal surface with coefficient of kinetic friction $\mu$ _k = 0.5. What is the change in entropy after the block has moved a distance of 1 m? The temperature of the block and surrounding is 22^$\circ$C.

A heat pump needs to supply 20 kW of power to maintain the inside temperature of a house at 25^$\circ$C while the outside temperature is 0^$\circ$C. What is the power needed for the heat pump?