Helium gas is subjected to a polytropic process in which the heat supplied to the gas is four times the work done by it. The molar heat capacity of the gas for the process is: (R is universal gas constant)

Question

Helium gas is subjected to a polytropic process in which the heat supplied to the gas is four times the work done by it. The molar heat capacity of the gas for the process is: (R is universal gas constant) (A) R/2 (B) R (C) 2 R (D) 3 R

Tardigrade Admin · Accepted Answer

Given, Δ Q=4 Δ W But, Δ W=Δ U=Δ Q ∴ Δ U=3 Δ W=(3/4) Δ Q ⇒ n CV Δ T=(3/4) n C Δ T or, C=(4/3) CV=(4/3)[(3 R/2)]=2 R

Q. Helium gas is subjected to a polytropic process in which the heat supplied to the gas is four times the work done by it. The molar heat capacity of the gas for the process is: $(R$ is universal gas constant)

R/2

R

2 R

3 R

Given, $Δ Q = 4Δ W$
But, $Δ W = Δ U = Δ Q$
$∴ Δ U = 3Δ W = \frac{3}{4} Δ Q$
$\Rightarrow n C_{V} Δ T = \frac{3}{4} n C Δ T$
or, $C = \frac{4}{3} C_{V} = \frac{4}{3} [\frac{3 R}{2}] = 2 R$

Q. Helium gas is subjected to a polytropic process in which the heat supplied to the gas is four times the work done by it. The molar heat capacity of the gas for the process is: (R is universal gas constant)

R/2

R

2 R

3 R

Given, ΔQ=4ΔW But, ΔW=ΔU=ΔQ ∴ΔU=3ΔW=43​ΔQ ⇒nCV​ΔT=43​nCΔT or, C=34​CV​=34​[23R​]=2R

Q. Helium gas is subjected to a polytropic process in which the heat supplied to the gas is four times the work done by it. The molar heat capacity of the gas for the process is: $(R$ is universal gas constant)

Given, $Δ Q = 4Δ W$
But, $Δ W = Δ U = Δ Q$
$∴ Δ U = 3Δ W = \frac{3}{4} Δ Q$
$\Rightarrow n C_{V} Δ T = \frac{3}{4} n C Δ T$
or, $C = \frac{4}{3} C_{V} = \frac{4}{3} [\frac{3 R}{2}] = 2 R$