A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is A and B respectively. Then the ratio, A : B is

Step-by-step solution

The first law of thermodynamics states that Q = U + W , where Q is the heat supplied, U is the change in internal energy, and W is the work done by the gas. For a monoatomic ideal gas undergoing a constant pressure process, the quantities are given by U = n C_v T with C_v = 3 2 R , W = n R T , and Q = n C_p T with C_p = 5 2 R . The percentage of heat used to increase internal energy is: A = U Q 100 = n (3R/2) T n (5R/2) T 100 = 3 5 100 = 60 % The percentage used for external work is: B = W Q 100 = n R T n (5R/2) T