Question

12 gms of gas occupies a volume of $4\times {10}^{-3}{m}^3$ at a temperature of $7^{\circ }C$. After the gas is heated at constant pressure its density becomes $6\times {10}^{-4}gm/cc$. The temperature to which the gas was heated is:

• A. 1000 K
• B. 1400 K
• C. 1200 K
• D. 800 K

Answer 1

The correct option is B 1400 K

$PV=nRT=\frac{w}{M}RT$
Hence, $P=\frac{\rho }{M}RT$
Initially, $PV=\frac{w}{M}R{T}_1$ ......(1)
After heating, $P=\frac{\rho }{M}R{T}_2$ ......(2)
From equations (1) and (2),
The temperature to which the gas was heated is $T_2=\frac{w{T}_1}{\rho V}=\frac{12\times 280}{6\times {10}^{-4}\times 4\times {10}^3}=1400$