Question

$10g$ of gas at $STP$ occupies $5$ litres. The temperature at which the volume becomes double for the same mass of gas at the same pressure is?

• A. $586K$
• B. $-{273}^{\circ }C$
• C. ${273}^{\circ }C$
• D. ${546}^{\circ }C$

Answer 1

The correct option is C ${273}^{\circ }C$

$\text{Given: At STP,}$

$\text{Temperature,}T=0^{\circ }C=273K$

$\text{Pressure,}P=1atm$

$10gm\left(\omega \right)\text{of gas occupied}5\text{litres}\left(V\right)$

$\text{here,}$

$\text{The volume becomes double for the same}$

$\text{mass(w) of gas and same pressure.}$

$Solution:\therefore by,PV=nRT$

$\left(V\alpha T\right)$

$\frac{V^{\prime }}{V}=\frac{T^{\prime }}{T}$

$\text{putting,}{V}^{\prime }=2V,T=273K$

$\text{\&}{T}^{\prime }=?\left(9n^{\circ }C\right)$

$\frac{2V}{V}=\frac{T^{\prime }}{273}$

$T^{\prime }=2\times 273K$

$T^{\prime }=(2\times 273-273{)}^{\circ }C$

$T^{\prime }=273(2-1)$

$(T^{\prime }={273}^{\circ }C)$

$\therefore \text{Correct option is (C)}$