Question

Follwing operation are carried out on a sample of ideal gas initially at pressure P volume V and kelvin temperature T.

a) At constant volume, the pressure is increased fourfold.

b) At constant pressure, the volume is doubled

c) The volume is doubled and pressure halved.

d) If heated in a vessel open to atmosphere, one-fourth of the gas escapes from the vessel.

Arrange the above operations in the increasing order of final temperature.

• A. a,b,c,d
• B. c,b,a,d
• C. b,a,d,c
• D. c,d,b,a

Answer 1

The correct option is D c,d,b,a

ideal gas equation

$PV=nRT$ eq(1)

where

$P$ = Pressure

$V$ = Volume

$n$ = number of moles

$R$ = universal gas constant

$T$ = Temperature

suppose initial values are $P_1,V_1,n_1,T_1$ and

final values are $P_2,V_2,n_2,T_2$

so

$P_1{V}_1=n_{1}R{T}_1$ eq(2)

$P_2{V}_2=n_{2}R{T}_2$ eq(3)

(a) At constant volume, the pressure is increased fourfold

$V_2=V_1$

$P_2=4P_1$

$n_2=n_1$

$\frac{eq\left(3\right)}{eq\left(2\right)}$

$\frac{T_2}{T_1}=4$

$T_2=4T_1$

(b) At constant pressure, the volume is doubled

$V_2=2V_1$

$P_2=P_1$

$n_2=n_1$

$\frac{eq\left(3\right)}{eq\left(2\right)}$

$\frac{T_2}{T_1}=2$

$T_2=2T_1$

(c) The volume is doubled and pressure halved.

$V_2=2V_1$

$P_2=\frac{1}{2}{P}_1$

$n_2=n_1$

$\frac{eq\left(3\right)}{eq\left(2\right)}$

$\frac{T_2}{T_1}=1$

$T_2=T_1$

(d) If heated in a vessel open to atmosphere, onefourth of the gas escapes from the vessel.

for open vessel pressure and volume will be constant.

$V_2=V_1$

$P_2=P_1$

one-fourth of gas escaped from vessel, so three-fourth gas left

$n_2=\frac{3}{4}{n}_1$

$\frac{\frac{3}{4}{T}_2}{T_1}=1$

$T_2=\frac{4}{3}{T}_1$

arranging final temperature in increasing order

(c),(d),(b),(a)