To find the heat given to a diatomic gas (\(γ = 1.4\)) during an isobaric process where it does \(400\) J of work, we apply the first law of thermodynamics: \( \Delta Q = \Delta U + W \), where \( \Delta Q \) is the heat added, \( \Delta U \) is the change in internal energy, and \( W \) is the work done by the gas. For an ideal diatomic gas undergoing an isobaric process, the change in internal energy \( \Delta U \) is related to the work done and specific heat capacities:
Number of degrees of freedom \( f = 5 \) (for a diatomic gas).
Using \( \gamma = \frac{C_p}{C_v} = 1.4 \), obtain \( C_v = \frac{R}{\gamma - 1} \) and \( C_p = C_v + R \).
Additional relationships:
\( \Delta U = nC_v\Delta T \) and \( \Delta Q = nC_p\Delta T \). Combining, \( \Delta Q = \Delta U + W = nC_v\Delta T + W.
