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Chapter 10: Problem 41
Use Avogadro's number to find the mass of a helium atom.
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Show that if the temperature on the Celsius scale changes by \(\Delta T_{C}\), the Fahrenheit temperature changes by \(\Delta T_{F}=\frac{9}{5} \Delta T_{C}\)
Two small containers, each with a volume of \(100 \mathrm{~cm}^{3}\), contain helium gas at \(0^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) pressure. The two containers are joined by a small open tube of negligible volume, allowing gas to flow from one container to the other. What common pressure will exist in the two containers if the temperature of one container is raised to \(100^{\circ} \mathrm{C}\) while the other container is kept at \(0^{\circ} \mathrm{C}\) ?
An expandable cylinder has its top connected to a spring with force constant \(2.00 \times 10^{3} \mathrm{~N} / \mathrm{m}\) (Fig. P10.60). The cylinder is filled with \(5.00 \mathrm{~L}\) of gas with the spring relaxed at a pressure of \(1.00 \mathrm{~atm}\) and a temperature of \(20.0^{\circ} \mathrm{C}\). (a) If the lid has a crosssectional area of \(0.0100 \mathrm{~m}^{2}\) and negligible mass, how high will the lid rise when the temperature is raised to \(250^{\circ} \mathrm{C}\) ? (b) What is the pressure of the gas at \(250^{\circ} \mathrm{C}\) ?
One mole of oxygen gas is at a pressure of \(6.00 \mathrm{~atm}\) and a temperature of \(27.0^{\circ} \mathrm{C}\). (a) If the gas is heated at constant volume until the pressure triples, what is the final temperature? (b) If the gas is heated so that both the pressure and volume are doubled, what is the final temperature?
Temperature differences on the Rankine scale are identical to differences on the Fahrenheit scale, but absolute zero is given as \(0^{\circ} \mathrm{R}\). (a) Find a relationship converting the temperatures \(T_{F}\) of the Fahrenheit scale to the corresponding temperatures \(T_{R}\) of the Rankine scale. (b) Find a second relationship converting temperatures \(T_{R}\) of the Rankine scale to the temperatures \(T_{K}\) of the Kelvin scale.
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