Question

If the pressure and the absolute temperature of a given mass of gas are doubled the new volume will be ___________the initial volume.

• A. same as
• B. doubles
• C. half
• D. four times

Answer 1

The correct option is A same as

Let initial pressure $=P_1$, Final pressure $P_2=2P_1.$

Initial temperature $=T_1,$ Final temperature $T_2=2T_1.$

Initial volume$=V,$ Final Volume$=V_2$.

From idea gas equation at constant no. of moles, $PV\propto T$

$\frac{P_1{V}_1}{P_2{V}_2}=\frac{T_1}{T_2}⟹\frac{P_1{V}_1}{2P_1{V}_2}=\frac{T_1}{2T_1}⟹\frac{V_1}{V_2}=1⟹V_1=V_2$

$\therefore$ Final Volume is same as initial volume.