As shown in the figure, a gas undergoes a process during which both its pressure and volume change. Let C be the molar heat capacity for this process.

Step-by-step solution

From the given p-V graph, as the process proceeds, both pressure ( p ) and volume ( V ) of the gas increase. Therefore, dp > 0 and dV > 0 . According to the ideal gas equation, pV = nRT . Differentiating both sides, we get: p dV + V dp = nR dT Since p, V, dp , and dV are all positive quantities, the change in temperature dT must also be positive ( dT > 0 ). From the first law of thermodynamics: dQ = dU + dW For n moles of gas, this can be written in terms of molar heat capacities as: n C dT = n C_V dT + p dV Dividi