÷ÈÓ°Ö±²¥

A 3.75 mole sample of an ideal gas with \(C_{V, m}=3 R / 2\) initially at a temperature \(T_{i}=298 \mathrm{K}\) and \(P_{i}=1.00\) bar is enclosed in an adiabatic piston and cylinder assembly. The gas is compressed by placing a \(725 \mathrm{kg}\) mass on the piston of diameter \(25.4 \mathrm{cm} .\) Calculate the work done in this process and the distance that the piston travels. Assume that the mass of the piston is negligible.

A 2.50 mole sample of an ideal gas, for which \(C_{V, m}=3 R / 2,\) is subjected to two successive changes in state: (1) From \(25.0^{\circ} \mathrm{C}\) and \(125 \times 10^{3} \mathrm{Pa}\), the gas is expanded isothermally against a constant pressure of \(15.2 \times 10^{3} \mathrm{Pa}\) to twice the initial volume. (2) At the end of the previous process, the gas is cooled at constant volume from \(25.0^{\circ} \mathrm{C}\) to \(-29.0^{\circ} \mathrm{C} .\) Calculate \(q, w, \Delta U,\) and \(\Delta H\) for each of the stages. Also calculate \(q, w, \Delta U,\) and \(\Delta H\) for the complete process.

Count Rumford observed that using cannon boring machinery a single horse could heat \(11.6 \mathrm{kg}\) of ice water \((T=273 \mathrm{K})\) to \(T=355 \mathrm{K}\) in 2.5 hours. Assuming the same rate of work, how high could a horse raise a 225 kg weight in 2.5 minutes? Assume the heat capacity of water is \(4.18 \mathrm{JK}^{-1} \mathrm{g}^{-1}\)

A 1.50 mole sample of an ideal gas at \(28.5^{\circ} \mathrm{C}\) expands isothermally from an initial volume of \(22.5 \mathrm{dm}^{3}\) to a final volume of \(75.5 \mathrm{dm}^{3} .\) Calculate \(w\) for this process (a) for expansion against a constant external pressure of \(1.00 \times 10^{5} \mathrm{Pa}\) and (b) for a reversible expansion.

Calculate \(w\) for the adiabatic expansion of \(2.50 \mathrm{mol}\) of an ideal gas at an initial pressure of 2.25 bar from an initial temperature of \(450 .\) K to a final temperature of \(300 .\) K. Write an expression for the work done in the isothermal reversible expansion of the gas at \(300 .\) K from an initial pressure of 2.25 bar. What value of the final pressure would give the same value of \(w\) as the first part of this problem? Assume that \(C_{P, m}=5 R / 2\)

In the reversible adiabatic expansion of 1.75 mol of an ideal gas from an initial temperature of \(27.0^{\circ} \mathrm{C}\), the work done on the surroundings is \(1300 .\) J. If \(C_{V, m}=3 R / 2,\) calculate \(q, w, \Delta U,\) and \(\Delta H\)

A 1.25 mole sample of an ideal gas is expanded from \(320 . \mathrm{K}\) and an initial pressure of 3.10 bar to a final pressure of 1.00 bar, and \(C_{P, m}=5 R / 2 .\) Calculate \(w\) for the following two cases: a. The expansion is isothermal and reversible. b. The expansion is adiabatic and reversible. Without resorting to equations, explain why the result to part (b) is greater than or less than the result to part (a).

A 2.25 mole sample of an ideal gas with \(C_{V, m}=3 R / 2\) initially at \(310 . \mathrm{K}\) and \(1.25 \times 10^{5}\) Pa undergoes a reversible adiabatic compression. At the end of the process, the pressure is \(3.10 \times 10^{6}\) Pa. Calculate the final temperature of the gas. Calculate \(q, w, \Delta U,\) and \(\Delta H\) for this process.

An ideal gas described by \(T_{i}=275 \mathrm{K}, P_{i}=1.10 \mathrm{bar}\) and \(V_{i}=10.0 \mathrm{L}\) is heated at constant volume until \(P=\) 10.0 bar. It then undergoes a reversible isothermal expansion until \(P=1.10\) bar. It is then restored to its original state by the extraction of heat at constant pressure. Depict this closed-cycle process in a \(P-V\) diagram. Calculate \(w\) for each step and for the total process. What values for \(w\) would you calculate if the cycle were traversed in the opposite direction?

A 1.75 mole sample of an ideal gas for which \(P=2.50\) bar and \(T=335 \mathrm{K}\) is expanded adiabatically against an external pressure of 0.225 bar until the final pressure is 0.225 bar. Calculate the final temperature, \(q, w, \Delta H\) and \(\Delta U\) for (a) \(C_{V, \text { m }}=3 R / 2,\) and (b) \(C_{V, m}=5 R / 2\)