When an ideal gas ( = 5 3 ) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?

Step-by-step solution

For an ideal gas heated at constant pressure, the heat supplied equals Q_p = nC_p T , while the work done is W = nR T . The ratio of work to heat input becomes W Q_p = R C_p . Using the specific heat ratio = C_p C_v and Mayer's relation C_p - C_v = R , we obtain C_p (1 - 1 ) = R . This yields R C_p = - 1 . Substituting = 5 3 gives 5 3 - 1 5 3 = 2 5 . The percentage of heat energy utilized in external work is 2 5 100 % = 40 % . Final Answer: D