Question

30 litre gas at 400 K and 300 atm pressure is compressed to a pressure of 600 atm and 200 K. The compressibility factor is changed from 1.2 to 1.6 respectively. Calculate the final volume of the gas.

Answer 1

Given: Initial volume of gas $V_1$ = 30L

Initial temperature of gas $T_1$=400K

Initial pressure of gas $P_1$=300atm

Initial compressibility factor $z_1$ = 1.2

Final pressure of gas $P_2$=600atm

Final temperature of gas $T_2$=200K

Final compressibility factor $z_2$ = 1.6

Solution: As we know the compressibility factor before compression given by,

$z_1=\frac{P_1{V}_1}{R{T}_1}$ (1)

After compression we get,

$z_2=\frac{P_2{V}_2}{R{T}_2}$ (2)

Now, on dividing equation (1) by equation (2) we get,

$\frac{z_1}{z_2}=\frac{P_1}{P_2}\times \frac{T_2}{T_1}\times \frac{V_1}{V_2}$

Substituting the values and solving we get,

$V_2=$=10L

Hence, the correct answer is 10L.