Chapter 23: Problem 20
What mass of steam at \(100^{\circ} \mathrm{C}\) must be mixed with \(150 \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\), in a thermally insulated container, to produce liquid water at \(50^{\circ} \mathrm{C}\) ?
Chapter 23: Problem 20
What mass of steam at \(100^{\circ} \mathrm{C}\) must be mixed with \(150 \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\), in a thermally insulated container, to produce liquid water at \(50^{\circ} \mathrm{C}\) ?
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Get started for freeA container holds a mixture of three nonreacting gases: \(n_{1}\) moles of the first gas with molar specific heat at constant volume \(C_{1}\), and so on. Find the molar specific heat at constant volume of the mixture, in terms of the molar specific heats and quantities of the three separate gases.
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 \(0.60 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\)
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.
Ice has formed on a shallow pond and a steady state has been reached with the air above the ice at \(-5.20^{\circ} \mathrm{C}\) and the bottom of the pond at \(3.98^{\circ} \mathrm{C}\). If the total depth of ice \(+\) water is \(1.42 \mathrm{~m}\), how thick is the ice? (Assume that the thermal conductivities of ice and water are \(1.67\) and \(0.502 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), respectively.)
(a) Two \(50-\mathrm{g}\) ice cubes are dropped into \(200 \mathrm{~g}\) of water in a glass. If the water were initially at a temperature of \(25^{\circ} \mathrm{C}\), and if the ice came directly from a freezer at \(-15^{\circ} \mathrm{C}\), what is the final temperature of the drink? ( \(b\) ) If only one ice cube had been used in (a), what would be the final temperature of the drink? Neglect the heat capacity of the glass.
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