An ideal gas with adiabatic exponent γ is heated at constant pressure. It absorbs Q amount of heat. Fraction of heat absorbed in increasing the temperature is

Question

An ideal gas with adiabatic exponent &gamma; is heated at constant pressure. It absorbs Q amount of heat. Fraction of heat absorbed in increasing the temperature is (A) &gamma; (B) (1/&gamma;) (C) 1-(1/&gamma;) (D) 2 &gamma;

Tardigrade Admin · Accepted Answer

Heat absorbed in increasing temperature =Δ U=Δ Q-Δ W=n CV Δ T Fraction of heat absorbed =( text Heat absorbed / text Total heat ) =(n CV Δ T/n CP Δ T) =(CV/CP)=(1/&gamma;)

Q. An ideal gas with adiabatic exponent $γ$ is heated at constant pressure. It absorbs $Q$ amount of heat. Fraction of heat absorbed in increasing the temperature is

$γ$

$\frac{1}{γ}$

$1 - \frac{1}{γ}$

$2 γ$

Heat absorbed in increasing temperature $= Δ U = Δ Q - Δ W = n C_{V} Δ T$
Fraction of heat absorbed $= \frac{Heat absorbed}{Total heat}$
$= \frac{n C _{V} Δ T}{n C _{P} Δ T}$
$= \frac{C _{V}}{C _{P}} = \frac{1}{γ}$

Q. An ideal gas with adiabatic exponent γ is heated at constant pressure. It absorbs Q amount of heat. Fraction of heat absorbed in increasing the temperature is

γ

γ1​

1−γ1​

2γ

Heat absorbed in increasing temperature =ΔU=ΔQ−ΔW=nCV​ΔT Fraction of heat absorbed = Total heat Heat absorbed ​ =nCP​ΔTnCV​ΔT​ =CP​CV​​=γ1​

Q. An ideal gas with adiabatic exponent $γ$ is heated at constant pressure. It absorbs $Q$ amount of heat. Fraction of heat absorbed in increasing the temperature is

$γ$

$\frac{1}{γ}$

$1 - \frac{1}{γ}$

$2 γ$

Heat absorbed in increasing temperature $= Δ U = Δ Q - Δ W = n C_{V} Δ T$
Fraction of heat absorbed $= \frac{Heat absorbed}{Total heat}$
$= \frac{n C _{V} Δ T}{n C _{P} Δ T}$
$= \frac{C _{V}}{C _{P}} = \frac{1}{γ}$