An ideal gas goes from an initial state to a final state such that its pressure is directly proportional to its volume. During this process, the volume of the gas increases. Which of the following statements are correct? A. The work done by the gas is positive. B. The heat added to the gas is equal to the change in its internal energy. C. The temperature of the gas increases. D. The internal energy of the gas increas

Step-by-step solution

Given that the pressure is directly proportional to the volume, P V , or P = kV where k is a positive constant. Since the volume of the gas increases, the gas expands. The work done by the gas is W = P dV . For an expansion process, dV > 0 , so the work done is positive (Statement A is correct). According to the ideal gas equation, PV = nRT . Substituting P = kV , we get kV^2 = nRT , which implies T V^2 . Since the volume increases, the temperature of the gas must also increase (Statement C is correct). As the temp