Question

A sample of a diatomic gas at pressure $p$, volume $V$ and temperature $T$ is compressed to $V/2$ isothermally. Its pressure is found to be $p_i$. If it is compressed to $V/2$ adiabatically, its pressure comes out to be $p_a$. What is the relation between $p_i$ and $p_a$?

• A. $p_i=p_a$
• B. $2p_i=p_a$
• C. $p_i=2.6p_a$
• D. $2.6p_i=2p_a$

Answer 1

The correct option is D $2.6p_i=2p_a$

Given : A sample of a diatomic gas at pressure pp, volume VV and temperature TT is compressed to V/2V/2 isothermally. Its pressure is found to be pipi. If it is compressed to V/2V/2 adiabatically, its pressure comes out to be papa. What is the relation between pipi and papa

Solution :

Case 1(Isothermal process)

$V_1=V$ , $V_2=\frac{V}{2}$ , $P_1=P$ , $P_2=P_i$

$P_1{V}_1=P_2{V}_2$

$PV=P_i\frac{V}{2}$

$P_i=2P$

Case 2(adiabatic process)

$V_1=V$ , $V_2=\frac{V}{2}$ , $P_1=P$ , $P_2=Pa$

$\gamma =1.4$

$P{V}^{\gamma }=constant$

$P{V}^{\gamma }=(P_a\frac{V}{2}{)}^{\gamma }$

$P_a=P(2{)}^{1.4}$

$P_a=2.6P$

The Correct Opt = D