Second law, heat engines and entropy

A heat engine has efficiency $0.35$ and produces $700\mathrm{J}$ of work in each cycle. Compute the heat absorbed and the heat released in one cycle.

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A refrigerator with coefficient of performance $\epsilon =5.0$ extracts $2.5\cdot 10^4\mathrm{J}$ from its interior. Compute the work spent and the heat released to the surroundings.

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A Carnot engine operates between $450\mathrm{K}$ and $300\mathrm{K}$ and absorbs $900\mathrm{J}$ per cycle. Compute the efficiency and the work produced in one cycle.

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A reversible engine releases heat to a reservoir at $290\mathrm{K}$. Compute the temperature of the hot reservoir needed to obtain an efficiency of $0.42$.

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A Carnot heat pump heats a house at $22{}^{\circ }\mathrm{C}$ taking heat from the outside at $0{}^{\circ }\mathrm{C}$, and it must deliver a thermal power of $5.0\mathrm{kW}$ to the house. Compute the coefficient of performance and the minimum mechanical power required.

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A manufacturer claims a freezer with coefficient of performance $9.0$ that keeps its interior at $255\mathrm{K}$ in a room at $295\mathrm{K}$. Determine whether the claim is compatible with the second law.

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$3.0\mathrm{kg}$ of water is heated from $10{}^{\circ }\mathrm{C}$ to $90{}^{\circ }\mathrm{C}$ ($c=4186J/(\mathrm{kg}\cdot \mathrm{K})$). Compute the change in entropy of the water.

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A heat of $5.0\mathrm{kJ}$ passes by conduction from a reservoir at $600\mathrm{K}$ to a reservoir at $300\mathrm{K}$. Compute the change in entropy of the universe.

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Compute the change in entropy of $0.20\mathrm{kg}$ of ice that melts at $0{}^{\circ }\mathrm{C}$ (${\lambda }_f=3.33\cdot 10^{5}J/kg$).

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Two moles of ideal gas expand isothermally and reversibly at $350\mathrm{K}$ from $10\mathrm{L}$ to $25\mathrm{L}$. Compute the change in entropy of the gas and the heat absorbed.

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In a rigid, insulated container $0.50\mathrm{mol}$ of ideal gas expands freely into vacuum until it occupies twice the initial volume. Compute the change in entropy of the universe.

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A monatomic ideal gas goes clockwise through a rectangular cycle in the $(V,p)$ plane formed by two isochoric processes at $3.0\mathrm{L}$ and $6.0\mathrm{L}$ and by two isobaric processes at $1.0\cdot 10^5\mathrm{Pa}$ and $2.0\cdot 10^5\mathrm{Pa}$. Compute the work per cycle and the efficiency.

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In an insulated container of negligible heat capacity $1.0\mathrm{kg}$ of water at $90{}^{\circ }\mathrm{C}$ and $1.0\mathrm{kg}$ of water at $10{}^{\circ }\mathrm{C}$ are mixed ($c=4186J/(\mathrm{kg}\cdot \mathrm{K})$). Compute the final temperature and the change in entropy of the universe.

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