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Chapter 17: Problem 9
Ice and water have been together in a glass for a long time. Is the water hotter than the ice?
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At high gas densities, the van der Waals equation modifies the ideal-gas law to account for nonzero molecular volume and for the van der Waals force that we discussed in Section \(17.1 .\) The van der Waals equation is $$\left(p+\frac{n^{2} a}{V^{2}}\right)(V-n b)=n R T$$ where \(a\) and \(b\) are constants that depend on the particular gas. For nitrogen \(\left(\mathrm{N}_{2}\right), a=0.14 \mathrm{Pa} \cdot \mathrm{m}^{6} / \mathrm{mol}^{2}\) and \(b=3.91 \times 10^{-5} \mathrm{m}^{3} / \mathrm{mol}\) For 1.000 mol of \(\mathrm{N}_{2}\) at 10.00 atm pressure, confined to a volume of \(2.000 \mathrm{L},\) find the temperatures predicted (a) by the ideal-gas law and (b) by the van der Waals equation.
Describe the composition and temperature of the equilibrium mixture after \(1.0 \mathrm{kg}\) of ice at \(-40^{\circ} \mathrm{C}\) is added to \(1.0 \mathrm{kg}\) of water at \(5.0^{\circ} \mathrm{C}\).
If a 1 -megaton nuclear bomb were exploded deep in the Greenland ice cap, how much ice would it melt? Assume the ice is initially at about its freezing point, and consult Appendix C for the appropriate energy conversion.
According to the ideal-gas law, what should be the volume of a gas at absolute zero? Why is this result absurd?
Two different gases are at the same temperature, and both have low enough densities that they behave like ideal gases. Do their molecules have the same thermal speeds? Explain.
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