A gas has molar heat capacity C = 37.55 J mole-1 K-1, in the process PT = constant. The number of degrees of freedom of the molecules of the gas.

Question

A gas has molar heat capacity C = 37.55 J mole-1 K-1, in the process PT = constant. The number of degrees of freedom of the molecules of the gas. (A) 6 (B) 3 (C) 1 (D) 5

Tardigrade Admin · Accepted Answer

Here, C = 37.55 J mole-1 K-1; and PT= K (constant) ...(i) According to standard gas equation PV = RT or P = RT/V From (i), (RT/V) × T = K or V = (RT2/K) ∴ (dV/dt) = (2RT/K) But (T/K) = (1/P) rom eqn. (i), therefore, (dV/dT) = (2R/P) ...(ii ) As, C = Cv + P (dV/dT), therefore, using (ii) C = Cv + P × (2R/P) = Cv + 2R or Cv=C - 2R As, Cv = (n/2) R ∴ (n/2)R = C - 2R or n = (2(C - 2R)/R) = (2(37.55-2×8.3)/8.3) = 5

Q. A gas has molar heat capacity $C = 37.55 J m o l e^{- 1} K^{- 1}$ , in the process $PT =$ constant. The number of degrees of freedom of the molecules of the gas.

$6$

$3$

$1$

$5$

Q. A gas has molar heat capacity C=37.55Jmole−1K−1, in the process PT= constant. The number of degrees of freedom of the molecules of the gas.

6

3

1

5

Q. A gas has molar heat capacity $C = 37.55 J m o l e^{- 1} K^{- 1}$ , in the process $PT =$ constant. The number of degrees of freedom of the molecules of the gas.

$6$

$3$

$1$

$5$