An ideal gas undergoes an isobaric expansion where it performs 830 J of work. If the molar heat capacity of the gas at constant volume is 20.75 J K ⁻¹ mol ⁻¹ , the total heat absorbed by the gas during this process is ________ J . (Given: R = 8.3 J K ⁻¹ mol ⁻¹ )

Step-by-step solution

The work done by an ideal gas during an isobaric process is: W = n R T n T = W R = 830 8.3 = 100 mol K The change in internal energy of the gas is: U = n C_ v,m T U = C_ v,m (n T) = 20.75 100 = 2075 J According to the first law of thermodynamics, the total heat absorbed q is: q = U + W q = 2075 + 830 = 2905 J Alternatively, using molar heat capacity at constant pressure: C_ p,m = C_ v,m + R = 20.75 + 8.3 = 29.05 J K ⁻¹ mol ⁻¹ q = n C_ p,m T = 29.05 100 = 2905 J Answer: 2905