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Chapter 24: Problem 13

A heat engine absorbs \(52.4 \mathrm{~kJ}\) of heat and exhausts \(36.2 \mathrm{~kJ}\) of heat each cycle. Calculate \((a)\) the efficiency and \((b)\) the work done by the engine per cycle.

Short Answer

Expert verified
The efficiency of the heat engine is approximately \(0.3085\) or \(30.85 \%\), and the work done per cycle is \(16.2 \, kJ\).

Step by step solution

01

Calculate the Efficiency

First, calculate the efficiency of the heat engine. This is done using the formula \(η = 1 - \frac{Q_{out}}{Q_{in}}\), where \(Q_{in} = 52.4 \, kJ\) is the heat absorbed and \(Q_{out} = 36.2 \, kJ\) is the heat exhausted. Substitute the given values to obtain the efficiency.
02

Calculate the Work Done

Next, calculate the work done by the heat engine per cycle. The formula is \(Work \, done = Q_{in} - Q_{out}\), where \(Q_{in} = 52.4 \, kJ\) and \(Q_{out} = 36.2 \, kJ\). Substitute the given values into the equation and calculate the work done.

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Most popular questions from this chapter

An ideal gas undergoes an isothermal expansion at \(77^{\circ} \mathrm{C}\) increasing its volume from \(1.3\) to \(3.4 \mathrm{~L}\). The entropy change of the gas is \(24 \mathrm{~J} / \mathrm{K}\). How many moles of gas are present?

How much work must be done to extract \(10.0 \mathrm{~J}\) of heat \((a)\) from a reservoir at \(7^{\circ} \mathrm{C}\) and transfer it to one at \(27^{\circ} \mathrm{C}\) by means of a refrigerator using a Carnot cycle; \((b)\) from one at \(-73^{\circ} \mathrm{C}\) to one at \(27^{\circ} \mathrm{C} ;(c)\) from one at \(-173^{\circ} \mathrm{C}\) to one at \(27^{\circ} \mathrm{C} ;\) and \((d)\) from one at \(-223^{\circ} \mathrm{C}\) to one at \(27^{\circ} \mathrm{C} ?\)

In a refrigerator the low-temperature coils are at a temperature of \(-13^{\circ} \mathrm{C}\) and the compressed gas in the condenser has a temperature of \(25^{\circ} \mathrm{C}\). Find the coefficient of performance of a Carnot refrigerator operating between these temperatures.

A refrigerator does \(153 \mathrm{~J}\) of work to transfer \(568 \mathrm{~J}\) of heat from its cold compartment. (a) Calculate the refrigerator's coefficient of performance. ( \(b\) ) How much heat is exhausted to the kitchen?

An ideal gas undergoes a reversible isothermal expansion at \(132^{\circ} \mathrm{C}\). The entropy of the gas increases by \(46.2 \mathrm{~J} / \mathrm{K}\). How much heat is absorbed?
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