Heat is supplied to a diatomic gas at constant pressure. The ratio of Q : U : W is [Given Q= heat supplied, U= change in internal energy, W= work done]

Step-by-step solution

For a diatomic gas at constant pressure: The degrees of freedom are f = 5 (3 translational + 2 rotational), so C_v = 5 2 R and C_p = C_v + R = 7 2 R . Using the ideal gas law and thermodynamic relations: U = n C_v T = 5 2 n R T W = P V = n R T Q = n C_p T = 7 2 n R T = U + W The ratio becomes 7 2 n R T : 5 2 n R T : n R T . Multiplying through by 2 to eliminate fractions gives 7:5:2 . Thus, Q: U: W = 7:5:2 . The correct choice is D .