Question

If the absolute temperature of a gas is doubled and the pressure is reduced to one-half, the volume of the gas will

• A. remain unchanged
• B. be doubled
• C. increase four-fold
• D. be reduced to $1/4th$

Answer 1

The correct option is C increase four-fold

We know that $\frac{P_1{V}_1}{T_1}$ = $\frac{P_2{V}_2}{T_2}$

Volume of the gas = v

Pressure $P_1$ = p

Pressure $P_2$ = $\frac{1p}{2}$

Temperature = $T_1$ = t

Temperature = $T_2$ = 2t

$V_2$ = $P_1{V}_1{T}_2/T_1$

= $(p\times v\times 2t)$ / $(2t\times p)$

= v

That means $V_2=V_1$

So it increases four-fold so C is the correct option.