Worksheet: Entropy Change in a Thermodynamic Process

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In this worksheet, we will practice calculating the change in the entropy of a system that results from various thermodynamic processes.

Q1:

Find the entropy change of 20 g of steam at a temperature of 100∘C when it condenses to water at the same temperature. Use a value of 2,257 kJ/kg for the latent heat of vaporization of water.

Q2:

A cube of ice with a mass of fifty grams and at a temperature of 0.00∘C is allowed to melt to become water and then to boil to become water vapor at 100∘C. What is the change in entropy of the water in this process?

Q3:

2.00×10 joules of heat is removed from a heat reservoir at a temperature of 2.00×10 K. What is the entropy change of the reservoir?

Q4:

A system consisting of 20.0 mol of a monoatomic ideal gas is cooled at constant pressure from a volume of 50.0 L to a volume of 10.0 L. The initial temperature of the gas was 300 K. What is the change in entropy of the gas? (Take universal gas constant to be 8.314 J⋅mol−1⋅K−1)

Q5:

An ideal gas at a temperature of 3.0×10 K is compressed isothermally to a volume that is 0.20 times its initial volume. Determine the entropy change per mole of the gas.

Q6:

A 2.00 × 102-g mass of water at a temperature of 0.00∘C is brought into thermal equilibrium successively with reservoirs at 20.0∘C, 40.0∘C, 60.0∘C, and 80.0∘C. Use a value of 4,182/⋅JkgC∘ for the specific heat capacity of water.

What is the entropy change of the water?

What is the entropy change of the reservoirs?

What is the entropy change of the universe?

Q7:

A Carnot engine operates between baths with temperatures of 550∘C and 20∘C, and extracts 300 kJ of energy in each cycle.

Find the change in entropy of the hot bath in each Carnot cycle.

Find the change in entropy of the cold bath in each Carnot cycle.

Q8:

A copper rod of cross-sectional area 5.0 cm2 and length 5.0 m conducts heat from a heat reservoir at 373 K to one at 273 K. What is the time rate of change of the universe’s entropy for this process? Use a value of 385 W/m⋅K for the thermal conductivity of copper.

  • A4.00×10 W/K
  • B2.50×10 W/K
  • C3.78×10 W/K
  • D2.88×10 W/K
  • E3.33×10 W/K

Q9:

A piece of aluminum of mass 0.50 kg is at a temperature of 250∘C. The aluminum is dropped into a 1.0 kg mass of water that is at a temperature of 20∘C. After equilibrium is reached, what is the net entropy change of the system? Use a value of 4,184/⋅JkgC∘ as the specific heat capacity of water and a value of 900/⋅JkgC∘ as the specific heat capacity of aluminum.

Q10:

A mass of water of 200 g that has a temperature of 0.00∘C is brought into contact with a heat reservoir at a temperature of 80.0∘C, and thermal equilibrium is reached. Take the specific heat capacity of water to be 4,180/⋅JkgC∘.

What is the temperature of the water?

What is the temperature of the reservoir?

How much heat has been transferred in the process?

  • A6.70×10 J
  • B7.00×10 J
  • C7.60×10 J
  • D7.20×10 J
  • E6.30×10 J

What is the entropy change of the water?

What is the entropy change of reservoir?

What is the entropy change of the universe?

Q11:

For the Carnot cycle in the figure, consider the efficiency to be 0.65 and the heat consumed per cycle to be 300 J.

What is the entropy change per cycle of the hot reservoir at 70∘C?

What is the entropy change per cycle of the cold reservoir?

Q12:

1.0 mol of an ideal gas is exactly tripled in volume by a reversible isothermal expansion in which the gas is heated by 1,300 J.

What is the change in entropy of the gas?

What is the temperature of the gas?

Q13:

A rock of mass 4.0 kg at a temperature of 23∘C is dropped vertically downward a distance of 1.2×10 m into a shallow lake that is also at a temperature of 23∘C.

What is the resulting change in the entropy of the universe?

If the temperature of the rock is 80∘C when it is dropped, what is the change in the entropy of the universe? Use a value of 4,184/⋅JkgC∘ for the specific heat of the lake’s water and use a value of 860/⋅JkgC∘ for the specific heat of the rock. Assume that the drag on the rock from the air is negligible.

Q14:

A pool of water of mass 40 g is at a temperature of 25∘C. The water is heated until it becomes vapor at 100∘C. Calculate the change in entropy of the water in this process. Use a value of 4,184/⋅JkgC∘ for the specific heat capacity of water and use a value of 2,256 kJ/kg for the latent heat of vaporization of water.

Q15:

In an isochoric process, 5.0 mol of monatomic ideal gas at a temperature of 300 K is heated until its temperature reaches 370 K. What is the entropy change of the gas due to the heating?

Q16:

A pool of water of mass 60 g is at a temperature of 5.0∘C. The water is heated by bringing it to thermal equilibrium with a reservoir at a temperature of 70∘C. In calculating the entropy changes resulting from this process, use a value of 4,184/⋅JkgC∘ for the specific heat capacity of water.

What is the entropy change of the reservoir due to the heating of the water?

What is the entropy change of the water due to the heating of the water?

What is the entropy change of the universe due to the heating of the water?

Q17:

A lump of ice at 0.0∘C has a mass of 20 g. The ice is heated by the air, which is at a temperature negligibly greater than 0.0∘C, until all of the ice melts. An identical lump of ice is heated by air at a temperature of 25∘C. In determining the entropy changes resulting from these processes, use a value of 4,184/⋅JkgC∘ for the specific heat capacity of water and use a value of 334 kJ/kg for the latent heat of fusion of ice.

What is the entropy change of the ice due to its melting by air at a temperature negligibly greater than 0.0∘C?

What is the entropy change of the air due to the ice’s melting at a temperature negligibly greater than 0.0∘C?

What is the entropy change of the universe due to the ice’s melting at a temperature negligibly greater than 0.0∘C?

What is the entropy change of the ice due to its melting by air at a temperature of 25∘C?

What is the entropy change of the air due to the ice’s melting at a temperature of 25∘C?

What is the entropy change of the universe due to the ice’s melting at a temperature of 25∘C?

Q18:

A 4.0 kg wood block starts with an initial speed of 9.0 m/s and slides across the floor until friction stops it. What is the approximate change in entropy of the universe? Assume that everything stays at a room temperature of 25∘C.

Q19:

A glass beaker has a mass of 350 g. The beaker contains 450 g of water that is at a temperature of 25∘C. The beaker is heated reversibly until the temperatures of both the beaker and the water are 60∘C. Find the total change in entropy of the beaker and the water due to their heating. Use a value of 4,184/⋅JkgC∘ for the specific heat capacity of water and use a value of 840/⋅JkgC∘ for the specific heat capacity of glass.

Q20:

Suppose 25 g of ice at a temperature of 0.0∘C is added to 250 g of water at a temperature of 65∘C. Using a value for the latent heat of fusion of ice of 334 kJ/kg and using a value of the specific heat capacity of ice of 4,184/⋅JkgC∘, find the total change in entropy of the mixture after it reaches thermal equilibrium.

Q21:

A cylinder contains 600 g of helium at a pressure of 100 atm and a temperature of 25.0∘C. The cylinder has a leaking valve and all the gas slowly escapes isothermally into the atmosphere. What is the change in entropy of the universe due to the leakage?

Q22:

Calculate the quality of steam at a pressure of 0.80 MPa and an entropy of 6.55 kJ/kg.

Q23:

Heat is added to a closed system to move the system from the state 𝑆 to the state 𝑆. For 𝑆, entropy =𝑠 and temperature =𝑇. For 𝑆, entropy =𝑠 and temperature =𝑇. What is the net heating of the system in this process if 𝑇=𝑇=𝑇?

  • A𝑇𝑠𝑠
  • B𝑇(𝑠−𝑠)
  • C𝑇(𝑠+𝑠)2
  • D𝑇(𝑠−𝑠)

Q24:

What is the change in entropy when 1.0 kmol gas at a pressure of 1.0 MPa and a temperature of 300 K expands to a volume where it has a pressure 0.10 MPa? Assume that the expansion is isothermal.

Q25:

A gas is heated isothermally by 25 kJ at a temperature of 350 K. How much does the gas increase in entropy? Answer to three significant figures.

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