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Chapter 10: Problem 39
What is the average kinetic energy of a molecule of oxygen at a temperature of \(300 \mathrm{~K}\) ?
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The density of gasoline is \(7.30 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}\) at \(0^{\circ} \mathrm{C}\). Its average coefficient of volume expansion is \(9.60 \times 10^{-4}\left({ }^{\circ} \mathrm{C}\right)^{-1}\), and note that \(1.00 \mathrm{gal}=0.00380 \mathrm{~m}^{3}\). (a) Calculate the mass of \(10.0 \mathrm{gal}\) of gas at \(0^{\circ} \mathrm{C}\). (b) If \(1.000 \mathrm{~m}^{3}\) of gasoline at \(0^{\circ} \mathrm{C}\) is warmed by \(20.0^{\circ} \mathrm{C}\), calculate its new volume. (c) Using the answer to part (b), calculate the density of gasoline at \(20.0^{\circ} \mathrm{C}\). (d) Calculate the mass of \(10.0\) gal of gas at \(20.0^{\circ} \mathrm{C}\). (e) How many extra kilograms of gasoline would you get if you bought \(10.0\) gal of gasoline at \(0^{\circ} \mathrm{C}\) rather than at \(20.0^{\circ} \mathrm{C}\) from a pump that is not temperature compensated?
The Golden Gate Bridge in San Francisco has a main span of length \(1.28 \mathrm{~km}\), one of the longest in the world. Imagine that a steel wire with this length and a cross-sectional area of \(4.00 \times 10^{-6} \mathrm{~m}^{2}\) is laid on the bridge deck with its ends attached to the towers of the bridge, on a summer day when the temperature of the wire is \(35.0^{\circ} \mathrm{C}\). (a) When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to \(-10.0^{\circ} \mathrm{C}\), what is the tension in the wire? Take Young's modulus for steel to be \(20.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}\). (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of \(3.00 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}\). At what temperature would the wire reach its elastic limit? (c) Explain how your answers to (a) and (b) would change if the Golden Gate Bridge were twice as long.
S Show that the coefficient of volume expansion \(\beta\), is related to the coefficient of linear expansion, \(\alpha\) through the expression \(\beta=3 \alpha\).
The density of helium gas at \(0^{\circ} \mathrm{C}\) is \(\rho_{0}=0.179 \mathrm{~kg} / \mathrm{m}^{3}\). The temperature is then raised to \(T=100^{\circ} \mathrm{C}\), but the pressure is kept constant. Assuming the helium is an ideal gas, calculate the new density \(\rho_{f}\) of the gas.
An air bubble has a volume of \(1.50 \mathrm{~cm}^{3}\) when it is released by a submarine \(100 \mathrm{~m}\) below the surface of a lake. What is the volume of the bubble when it reaches the surface? Assume the temperature and the number of air molecules in the bubble remain constant during its ascent.
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