Worksheet: Entropy and the Second and Third Laws of Thermodynamics

In this worksheet, we will practice calculating the entropy of systems and the entropy change of systems that transfer internal energy to each other.

Q1:

Which of the following statements correctly expresses the relationship between the work done by a heat engine, 𝑊, and the internal energy lost by the heat engine’s high-temperature reservoir, Δ𝑄?

  • AΔ𝑄<𝑊
  • BΔ𝑄>𝑊
  • CΔ𝑄=𝑊

Q2:

At what constant temperature is a gas maintained at if the gas increases its internal energy by 45 kJ and its entropy increases by 125 J/K?

Q3:

Work done on an object can heat the object by dissipation. A heat engine can use heating of an object to do work.

When work is done on an object, what is the lowest number of joules dissipated per joule of work done?

When work is done on an object, what is the greatest number of joules dissipated per joule of work done?

For a heat engine that has the highest possible efficiency for a heat engine, what is the lowest number of joules of work per joule of input heating that the heat engine cannot output?

When a heat engine operates, what is the greatest number of joules of work done that cannot be supplied per joule of heating?

Which of the following changes in the net entropy of the systems involved in energy transfers, including energy transfers from the systems to their surroundings, can occur?

  • AEntropy increases.
  • BEntropy remains constant.
  • CEntropy increases, decreases, or remains constant.
  • DEntropy increases or remains constant.

Q4:

Water at a temperature of 100C changes state, requiring 2,260 J per gram of water that changes to steam. If 175 g of water is converted to steam, how much more entropy does the steam have than the water? Answer in kilojoules per kelvin to three significant figures.

Q5:

Calculate the magnitude of the heating of a gas at a temperature of 550 K that increases the entropy of the gas by 230 J/K. Answer in kilojoules to three significant figures.

Q6:

A heat engine has reservoir temperatures of 350 K and 300 K. The high-temperature reservoir heats the low-temperature reservoir by 5,000 J.

What is the entropy change of the low-temperature reservoir? Answer to three significant figures.

What is the entropy change of the high-temperature reservoir? Answer to three significant figures.

What is the entropy change of the surrounding environment? Answer to three significant figures.

Q7:

A box with four sides contains a gas consisting of only four particles, all of which have the same speeds and masses as each other. At a given time, each particle collides with any of the box’s sides. For pressure on all the sides of the box to be equal, one particle collides with each side of the box, as shown in the diagram. The entropy of the gas depends partly on Boltzmann’s constant, 1.3806×10 m2⋅kg/s2⋅K.

What is the difference in entropy between the state when the gas’s pressure is equal on all the box’s sides and the state when all the particles are colliding with a single side of the box? Answer to three significant figures.

  • A2.87×10 J/K
  • B4.53×10 J/K
  • C1.38×10 J/K
  • D2.47×10 J/K
  • E1.91×10 J/K

If the box contains 100 particles, what is the difference in entropy between the state when the gas’s pressure is equal on all the box’s sides and the state when all the particles are colliding with a single side of the box? Answer to three significant figures.

  • A2.76×10 J/K
  • B4.44×10 J/K
  • C2.34×10 J/K
  • D6.36×106 J/K
  • E1.38×10 J/K

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