How much heat does 2.5 mol of nitrogen need to warm by 35 K (a) in a rigid tank and (b) at a steady…

Step 1. Rigid tank. $Q = 2.5\ \text{mol} \times 20.775\ \text{J mol}^{-1}\text{K}^{-1} \times 35\ \text{K} = 1818\ \text{J}$.

Step 2. Steady pressure. $Q = 2.5\ \text{mol} \times 29.085\ \text{J mol}^{-1}\text{K}^{-1} \times 35\ \text{K} = 2545\ \text{J}$.

Step 3. Why. The extra $727\ \text{J}$ is the work $2.5\ \text{mol} \times 8.31\ \text{J mol}^{-1}\text{K}^{-1} \times 35\ \text{K}$ the gas does pushing the piston out.