B.4 熱力學（HL）：練習題

Which of the following is a direct consequence of the second law of thermodynamics for a cyclic process?

In an adiabatic compression of an ideal gas, the temperature of the gas increases. Which of the following correctly explains this observation using the first law of thermodynamics?

A fixed mass of an ideal gas undergoes a cycle represented on a \(P-V\) diagram by a rectangle. The vertices are at \((P_1, V_1)\), \((P_1, V_2)\), \((P_2, V_2)\), and \((P_2, V_1)\), where \(P_2 > P_1\) and \(V_2 > V_1\). If the cycle is performed in the counter-clockwise direction, what is the net work done by the gas and the net heat flow into the gas?

A gas is kept at a constant pressure of \(1.5 \times 10^5 \text{ Pa}\). During a thermodynamic process, the gas undergoes a volume change of \(-0.02 \text{ m}^3\). What is the work done by the gas?

An ideal gas is taken from state A to state B along two different paths in a \(P-V\) diagram. Which of the following quantities must be the same for both paths?

A fixed mass of 0.050 mol of an ideal gas is taken through a cycle ABCA. Process AB is an isothermal expansion at 400 K from \( V_A = 1.0 \times 10^{-3} \, \text{m}^3 \) to \( V_B = 3.0 \times 10^{-3} \, \text{m}^3 \). Process BC is an isovolumetric cooling. Process CA is an isobaric compression back to state A.

(a) Calculate the work done by the gas during the process AB.
(b) Determine the pressure at state C.
(c) Calculate the net work done during the entire cycle.

(a) A cylinder contains 0.20 mol of an ideal monatomic gas at an initial volume of \( 4.0 \times 10^{-3} \, \text{m}^3 \) and a temperature of 300 K. The gas undergoes an adiabatic expansion to a volume of \( 8.0 \times 10^{-3} \, \text{m}^3 \). Calculate the final temperature of the gas, given that for a monatomic gas \( \gamma = 5/3 \).

(b) Sketch the P-V diagram for this process and explain why the work done by the gas during an adiabatic expansion results in a decrease in internal energy.