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Chapter 23: Problem 41
A sample of \(n\) moles of an ideal gas undergoes an isothermal expansion. Find the heat flow into the gas in terms of the initial and final volumes and the temperature.
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a) Calculate the rate at which body heat flows out through the clothing of a skier, given the following data: the body surface area is \(1.8 \mathrm{~m}^{2}\) and the clothing is \(1.2 \mathrm{~cm}\) thick; skin surface temperature is \(33^{\circ} \mathrm{C}\), whereas the outer surface of the clothing is at \(1.0^{\circ} \mathrm{C} ;\) the thermal conductivity of the clothing is \(0.040 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K} .(b)\) How would the answer change if, after a fall, the skier's clothes become soaked with water? Assume that the thermal conductivity of water is \(0.60 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\)
A quantity of ideal monatomic gas consists of \(n\) moles initially at temperature \(T_{1}\). The pressure and volume are then slowly doubled in such a manner as to trace out a straight line on the \(p V\) diagram. In terms of \(n, R\), and \(T_{1}\), find \((\) a) \(W,(b)\) \(\Delta E_{\text {int }}\), and \((c) Q .(d)\) If one were to define an equivalent specific heat for this process, what would be its value?
A small electric immersion heater is used to boil \(136 \mathrm{~g}\) of water for a cup of instant coffee. The heater is labeled 220 watts. Calculate the time required to bring this water from \(23.5^{\circ} \mathrm{C}\) to the boiling point, ignoring any heat losses.
The average rate at which heat flows out through the surface of the Earth in North America is \(54 \mathrm{~mW} / \mathrm{m}^{2}\) and the average thermal conductivity of the near surface rocks is \(2.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Assuming a surface temperature of \(10^{\circ} \mathrm{C}\), what should be the temperature at a depth of \(33 \mathrm{~km}\) (near the base of the crust)? Ignore the heat generated by radioactive elements; the curvature of the Earth can also be ignored.
Consider that \(214 \mathrm{~J}\) of work are done on a system, and \(293 \mathrm{~J}\) of heat are extracted from the system. In the sense of the first law of thermodynamics, what are the values (including algebraic signs) of \((a) W,(b) Q\), and \((c) \Delta E_{\text {int }} ?\)
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