Question

The pressure and density of a diatomic gas ($\gamma =7/5$) change from $(P_1,d_1)to(P_2,d_2)$ adiabatically . If $d_2/d_1=32$, then what is the value of $P_2/P_1$?

• A. $\frac{P}{P^{\prime }}=\frac{1}{128}$
• B. $\frac{V^{\prime }}{V}=\frac{1}{128}$
• C. $\frac{P}{P^{\prime }}=128$
• D. $\frac{V^{\prime }}{V}=32$

Answer 1

The correct option is C $\frac{P}{P^{\prime }}=128$

Given : The pressure and density of a diatomic gas (γ=7/5γ=7/5) change from (P1,d1)to(P2,d2)(P1,d1)to(P2,d2) adiabatically . If d2/d1=32d2/d1=32, then what is the value of P2/P1P2/P1?

Solution :

We know that for adiabatic process $P{V}^{\gamma }=constant$

As $Density=\frac{mass}{volume}$

Then $\frac{V_1}{V_2}=\frac{d_2}{d_1}$

Hence we can say that $\frac{P_1}{P_2}=(\frac{d_2}{d_1}{)}^{\gamma }$

$\frac{P_1}{P_2}=(\frac{1}{32}{)}^{\frac{7}{5}}$

$\frac{P_2}{P_1}=128$

The Correct Opt=C