Question

If during an adiabatic process the pressure of mixture of gases is found to be proportional to square of its absolute temperature. The ratio of $C_P/C_V$ for mixture of gases is

• A. $2$
• B. $1.5$
• C. $1.67$
• D. $2.1$

Answer 1

The correct option is A $2$

For an adiabatic process, the expression is $P{V}^{\gamma }=const$
As, $PV=nRT$
$⟹P{\left(\frac{nRT}{P}\right)}^{\gamma }=const$
$⟹P^{1-\gamma }\cdot T^{\gamma }=const$
Given, $P\propto T^{-2}$
$⟹P{T}^{-2}=const$
$⟹P\cdot T^{\gamma /1-\gamma }=const$
$⟹\frac{\gamma }{\gamma -1}=+2$
$⟹\gamma =-2(1-\gamma )$
$⟹\gamma =2$