MHT CET202519 Apr 2025Morning ShiftPhysicsKinetic Theory of GasesActual
The molar specific heat of an ideal gas at constant pressure and constant volume is ' C _ p ' and ' C _ V ' respectively. If ' R ' is a universal gas constant and the ratio of ' C _ p ' to ' C _ V ' is , then ' C _ p ' is equal to
Options
- A( -1 +1 ) R
- B( -1) R
- CR ( -1)
- DR ( +1)
Correct answer
C. R ( -1)
Step-by-step solution
The molar specific heat at constant pressure C p for an ideal gas is derived using two fundamental relations. Mayer's relation gives C_p - C_v = R , where R is the universal gas constant. The ratio of specific heats is defined as = C_p / C_v . Expressing C_v in terms of C_p and yields C_v = C_p / . Substituting into Mayer's relation: C_p - C_p / = R . Factoring produces C_p (1 - 1/ ) = R , which simplifies to C_p ( - 1 ) / = R . Solving for C_p gives the final result: C_p = R - 1 This expression corresponds to opti