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

Question

An ideal gas is heated at constant pressure and absorbs amount of heat Q. If the adiabatic exponent is &gamma; , then the fraction of heat absorbed in raising the internal energy and 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=n Cp Δ T and change in internal energy Δ U = nCV Δ T W = Q -Δ U fraction =(W/Q)=(Q-Δ U/Q)=1-(Δ U/Q) =1-(Δ U/Q)=(1-(1/&gamma;))

Q. An ideal gas is heated at constant pressure and absorbs amount of heat $Q$ . If the adiabatic exponent is $γ$ , then the fraction of heat absorbed in raising the internal energy and 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 $Q = n C_{p} Δ T$ and change in internal energy
$Δ U = n C_{V} Δ T$
$W = Q - Δ U$
fraction $= \frac{W}{Q} = \frac{Q - Δ U}{Q} = 1 - \frac{Δ U}{Q}$
$= 1 - \frac{Δ U}{Q} = (1 - \frac{1}{γ})$

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

1−γ1​

1+γ1​

1−γ2​

1+γ2​