An ideal gas is heated at constant pressure and in this process, it absorbs Q amount of heat. If the adiabatic exponent is γ , then the fraction of heat absorbed in performing the work is

Question

An ideal gas is heated at constant pressure and in this process, it absorbs Q amount of heat. If the adiabatic exponent is &gamma; , then the fraction of heat absorbed in performing the work is (A) 1-(1/&gamma; ) (B) 1+(1/&gamma; ) (C) 1-(2/&gamma; ) (D) 1+(2/&gamma; )

Tardigrade Admin · Accepted Answer

Heat absorbed by the system at constant pressure Q=ncpΔ T Change in internal energy Δ U=ncvΔ T W=Q-Δ U ∴ (W/Q)=(Q - Δ U/Q)=1-(Δ U/Q) =1-(n cv Δ T/n cp Δ T)=1-(cv/cp) =(1 - (1/&gamma; ))

Q. An ideal gas is heated at constant pressure and in this process, it absorbs $Q$ amount of heat. If the adiabatic exponent is $γ$ , then the fraction of heat absorbed in performing the work is

$1 - \frac{1}{γ}$

$1 + \frac{1}{γ}$

$1 - \frac{2}{γ}$

$1 + \frac{2}{γ}$

Heat absorbed by the system at constant pressure
$Q = n c_{p} Δ T$
Change in internal energy $Δ U = n c_{v} Δ T$
$W = Q - Δ U$
$∴ \frac{W}{Q} = \frac{Q - Δ U}{Q} = 1 - \frac{Δ U}{Q}$
$= 1 - \frac{n c _{v} Δ T}{n c _{p} Δ T} = 1 - \frac{c _{v}}{c _{p}}$
$= (1 - \frac{1}{γ})$

Q. An ideal gas is heated at constant pressure and in this process, it absorbs Q amount of heat. If the adiabatic exponent is γ , then the fraction of heat absorbed in performing the work is

1−γ1​

1+γ1​

1−γ2​

1+γ2​