The molar heat capacity for an ideal gas at constant pressure is 20.785 J K -1 mol -1. The change in internal energy is 5000 J upon heating it from 300 K to 500 K. The number of moles of the gas at constant volume is [Nearest integer] (Given: R =8.314 J K -1 mol -1 )

Question

The molar heat capacity for an ideal gas at constant pressure is 20.785 J K -1 mol -1. The change in internal energy is 5000 J upon heating it from 300 K to 500 K. The number of moles of the gas at constant volume is [Nearest integer] (Given: R =8.314 J K -1 mol -1 ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

C p , m = C v , m + R ⇒ C v , m =20.785-8.314=12.471 J k -1 ml -1 Δ U = nC v , m Δ T ⇒ n =(5000/12.471 × 200)=(25/12.471) ≈ 2

Q. The molar heat capacity for an ideal gas at constant pressure is 20.785JK−1mol−1. The change in internal energy is 5000J upon heating it from 300K to 500K. The number of moles of the gas at constant volume is _____ [Nearest integer] (Given: R=8.314JK−1mol−1 )

Cp,m​=Cv,m​+R ⇒Cv,m​=20.785−8.314=12.471Jk−1ml−1 ΔU=nCv,m​ΔT ⇒n=12.471×2005000​=12.47125​≈2

$C_{p, m} = C_{v, m} + R$
$\Rightarrow C_{v, m} = 20.785 - 8.314 = 12.471 J k^{- 1} m l^{- 1}$
$Δ U = n C_{v, m} Δ T$
$\Rightarrow n = \frac{5000}{12.471 \times 200} = \frac{25}{12.471} \approx 2$