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Chapter 24: Problem 31

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.

Short Answer

Expert verified
The coefficient of performance of a Carnot refrigerator operating between the temperature of -13°C in the low-temperature coils and 25°C in the compressed gas in the condenser is the result of the continued fraction 260.15 K divided by the difference of 298.15 K and 260.15 K.

Step by step solution

01

Convert temperatures to Kelvin

Temperatures are given in Celsius. However, in thermodynamic temperature calculations, it's necessary to use the Kelvin scale. Convert the temperatures as: \(T_c = -13^{\circ} \mathrm{C} + 273.15 = 260.15 K\) and \(T_h = 25^{\circ} \mathrm{C} + 273.15 = 298.15 K\)
02

Calculate Coefficient of Performance

The formula for coefficient of performance (COP) of a Carnot refrigerator is given by: \(COP = T_c / (Th - Tc)\). Substituting the values calculated from Step 1, we get: \(COP = 260.15 K /(298.15 K - 260.15 K)\)
03

Simplify and Find Coefficient of Performance

Perform the arithmetic operation in the formula to get the Coefficient of Performance. This value indicates the efficiency of the Carnot refrigerator operating between the given temperatures.

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Most popular questions from this chapter

In a Carnot cycle, the isothermal expansion of an ideal gas takes place at \(412 \mathrm{~K}\) and the isothermal compression at \(297 \mathrm{~K}\). During the expansion, \(2090 \mathrm{~J}\) of heat energy are transferred to the gas. Determine \((a)\) the work performed by the gas during the isothermal expansion, ( \(b\) ) the heat rejected from the gas during the isothermal compression, and \((c)\) the work done on the gas during the isothermal compression.

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.

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 \(27^{\circ} \mathrm{C} ?\)

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?

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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