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Chapter 8: Problem 1192

An ideal refrigerator has a freezer at a temperature of \(-13\) C, The coefficient of performance of the engine is 5 . The temperature of the air to which heat is rejected will be. (A) \(325^{\circ} \mathrm{C}\) (B) \(39^{\circ} \mathrm{C}\) (C) \(325 \mathrm{~K}\) (D) \(320^{\circ} \mathrm{C}\)

Short Answer

Expert verified
The temperature of the air to which heat is rejected will be (B) \(39^{\circ} \mathrm{C}\).

Step by step solution

01

Convert freezer temperature from Celsius to Kelvin

First, we need to convert the freezer temperature from Celsius to Kelvin using the following formula: Tc (in Kelvin) = Tc (in Celsius) + 273.15 Tc = -13 + 273.15 = 260.15 K
02

Re-write the formula for the COP

Now, we re-write the formula for the coefficient of performance (COP) and arrange it to solve for Th (temperature of hot reservoir): COP = (Tc) / (Th - Tc) We are given the COP as 5. Thus, the equation becomes: 5 = (260.15) / (Th - 260.15)
03

Solve for Th

Solve for Th: 5(Th - 260.15) = 260.15 Th - 260.15 = 52.03 Th = 312.18 K
04

Convert Th from Kelvin to Celsius

Finally, convert the Th from Kelvin to Celsius: Temperature of the air in Celsius = Th (in Kelvin) - 273.15 Temperature of the air in Celsius = 312.18 - 273.15 = 39.03 °C Since the question asks for the temperature of the air to which the heat is rejected, we round the result to closest integer, that is, Temperature of the air = 39 °C So the correct answer is (B) \(39^{\circ} \mathrm{C}\).

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Most popular questions from this chapter

In a container of negligible heat capacity, \(200 \mathrm{~g}\) ice at \(0^{\circ} \mathrm{C}\) and \(100 \mathrm{~g}\) steam at \(100^{\circ} \mathrm{C}\) are added to \(200 \mathrm{~g}\) of water that has temperature $55^{\circ} \mathrm{C}$. Assume no heat is lost to the surroundings and the pressure in the container is constant \(1 \mathrm{~atm} .\) Amount of the Sm left in the system, is equal to (A) \(16.7 \mathrm{~g}\) (B) \(8.4 \mathrm{~g}\) (C) \(12 \mathrm{~g}\) (D) \(0 \mathrm{~g}\) Copyright () StemEZ.com. All rights reserved.

One mole of a monoatomic gas is heat at a constant pressure of 1 atmosphere from \(0 \mathrm{k}\) to \(100 \mathrm{k}\). If the gas constant $\mathrm{R}=8.32 \mathrm{~J} / \mathrm{mol} \mathrm{k}$ the change in internal energy of the gas is approximate ? (A) \(23 \mathrm{~J}\) (B) \(1.25 \times 10^{3} \mathrm{~J}\) (C) \(8.67 \times 10^{3} \mathrm{~J}\) (D) \(46 \mathrm{~J}\)

Air is filled in a motor tube at \(27^{\circ} \mathrm{C}\) and at a Pressure of 8 atmosphere. The tube suddenly bursts. Then what is the temperature of air. given \(\gamma\) of air \(=1.5\) (A) \(150 \mathrm{~K}\) (B) \(150^{\circ} \mathrm{C}\) (C) \(75 \mathrm{~K}\) (D) \(27.5^{\circ} \mathrm{C}\)

In a container of negligible heat capacity, 200 g ice at $0^{\circ} \mathrm{C}\( and \)100 \mathrm{~g}\( steam at \)100^{\circ} \mathrm{C}$ are added to \(200 \mathrm{~g}\) of water that has temperature \(55^{\circ} \mathrm{C}\). Assume no heat is lost to the surroundings and the pressure in the container is constant \(1 \mathrm{~atm}\). At the final temperature, mass of the total water present in the system is (A) \(493.6 \mathrm{~g}\) (B) \(483.3 \mathrm{~g}\) (C) \(472.6 \mathrm{~g}\) (D) \(500 \mathrm{~g}\)

An ideal gas heat engine is operating between \(227^{\circ} \mathrm{C}\) and \(127^{\circ} \mathrm{C}\). It absorbs \(10^{4} \mathrm{~J}\) Of heat at the higher temperature. The amount of heat Converted into. work is \(\ldots \ldots\) J. (A)2000 (B) 4000 (C) 5600 (D) 8000
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