Question

C_v and C_p denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then, 

(A) C_p -  C_v is larger for a diatomic ideal gas than for a monoatomic ideal gas

(B) C_P + C_V is larger for a diatomic ideal gas than for a monoatomic ideal gas

(C) C_p/C_v  is larger for a diatomic ideal gas than for a monoatomic ideal gas

(D) C_p *C_v is larger for a diatomic ideal gas than for a monoatomic ideal gas

Answer 1

Correct option (B, D) 

Explanation:

In case of free expansion under adiabatic conditions, change in internal energy ΔU = 0

∴ Internal energy and temperature will remain constant. 

 

If volume is doubled, temperature will decrease as per equation 

(ii). Further, molar heat capacity in process PV^x = constant is 

Since, molar heat capacity is positive, according to Q = nCΔT, Q will be negative if ΔT is negative. Or gas loses heat if temperature is decreasing.

Further, with increase in volume temperature will decrease.

As molar heat capacity is negative, Q will be positive if ΔT is negative. Or gas gains heat with decrease in temperature. 

(D) T ∝ PV

In expansion from V₁ to 2V₁ , product of PV is increasing. Therefore, temperature will increase. Or ΔU = +ve. Further, in expansion work done is also positive. 

Hence, Q = W + ΔU = +ve or, gas gains heat.