Serway & Jewett — The First Law of Thermodynamics: Problem 31.

You have a particular interest in automobile engines, so you have secured a co-op position at an automobile company while you attend school. Your supervisor is helping you to learn about the operation of an internal combustion engine. She gives you the following assignment, related to a simulation of a new engine she is designing. A gas, beginning at \(P_A = 1.00 \text{ atm}\), \(V_A = 0.500 \text{ L}\), and \(T_A = 27.0^\circ\text{C}\), is compressed from point A on the PV diagram in Figure P19.31 (page 530) to point B. This represents the compression stroke in a four-cycle gasoline engine. At that point, \(132 \text{ J}\) of energy is delivered to the gas at constant volume, taking the gas to point C. This represents the transformation of potential energy in the gasoline to internal energy when the spark plug fires. Your supervisor tells you that the internal energy of a gas is proportional to temperature (as we shall find in Chapter 20), the internal energy of the gas at point A is \(200 \text{ J}\), and she wants to know what the temperature of the gas is at point C.