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Chapter 19: Problem 1

Could you cool the kitchen by leaving the refrigerator open? Explain.

Short Answer

Expert verified
No, you could not cool the kitchen by leaving the refrigerator open. In fact, the opposite occurs - the overall heat in the kitchen would actually increase as the refrigerator's motor would end up producing more heat in its effort to cool the larger 'inside' space.

Step by step solution

01

Understand the process of a refrigerator

A refrigerator operates by using the laws of thermodynamics where it removes heat from the contents inside it and releases it outside to the surrounding area such as the kitchen. This is the principle of heat transfer, where heat moves from a region of higher temperature to one of lower temperature. The inside of the refrigerator becomes cooler as a result of this heat removal.
02

Analyzing the situation of an open refrigerator

When the refrigerator door is left open, the refrigerator will try to cool down the entire kitchen instead of just the space inside it. It will continuously operate to extract heat from the kitchen and expel it back into the kitchen itself. This is because the refrigerator doesn't have an outlet to push the heat to a region outside the kitchen. This process actually increases the total energy usage of the refrigerator.
03

Evaluating the overall effect

So, while the area immediately around the open fridge may feel cooler, the refrigerator's motor will end up producing more heat overall in its effort to cool the new, much larger 'inside' space. This happens because it will need to work even harder to maintain a cooler temperature, and in doing so, will produce more heat externally. Hence the heat emitted by the motor would surpass any possible cooling effect caused by the open refrigerator.

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Most popular questions from this chapter

A cosmic heat engine might operate between the Sun's \(5800 \mathrm{~K}\) surface and the \(2.7 \mathrm{~K}\) temperature of intergalactic space. What would be its maximum efficiency?

(a) Continue the calculation begun on page 372 in the subsection "Irreversible Heat Transfer" to derive the expression given in the text for the entropy change when equal masses \(m\) of hot and cold water, at temperatures \(T_{\mathrm{h}}\) and \(T_{c}\), respectively, are mixed: \(\Delta S=m c \ln \left[\left(T_{c}+T_{\mathrm{h}}\right)^{2} / 4 T_{\mathrm{c}} T_{\mathrm{h}}\right]\). (b) Show that the argument of the logarithm in this expression is greater than 1 for \(T_{\mathrm{h}} \neq T_{c}\), thus showing that \(\Delta S\) is positive. Hint: This is equivalent to showing that \(\left(T_{c}+T_{\mathrm{h}}\right)^{2}>4 T_{\mathrm{c}} T_{\mathrm{h}}\). Expand the left side of this inequality, subtract \(4 T_{\mathrm{c}} T_{\mathrm{h}}\) from both sides, factor the resulting left side, and you'll have your result.

The molar specific heat at constant pressure for a certain gas is given by \(C_{p}=a+b T+c T^{2}\), where \(a=33.6 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\), \(b=2.93 \times 10^{-3} \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}^{2}\), and \(c=2.13 \times 10^{-5} \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}^{3}\). Find the entropy change when \(2.00\) moles of this gas are heated from \(20.0^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\).

Problem 76 of Chapter 16 provided an approximate expression for the specific heat of copper at low absolute temperatures: \(c=31(T / 343 \mathrm{~K})^{3} \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\). Use this to find the entropy change when \(40 \mathrm{~g}\) of copper are cooled from \(25 \mathrm{~K}\) to \(10 \mathrm{~K}\). Why is the change negative?

A power plant extracts energy from steam at \(280^{\circ} \mathrm{C}\) and delivers \(880 \mathrm{MW}\) of electric power. It discharges waste heat to a river at \(30^{\circ} \mathrm{C}\). The plant's overall efficiency is \(29 \%\). (a) How does this efficiency compare with the maximum possible at these temperatures? (b) Find the rate of waste-heat discharge to the river. (c) How many houses, each requiring \(23 \mathrm{~kW}\) of heating power, could be heated with the waste heat from this plant?
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