Question

When a gas-filled in a closed vessel is heated through $1 \,{}^\circ C$ , its pressure increases by $0.4\%$ . The initial temperature of the gas was

• A. $250K$
• B. $2500K$
• C. $250^\circ C$
• D. $25 \,{}^\circ C$

Answer 1

Answer: (A)

$p_{1}=p \, and \, T_{1}=T \, ;$
$p_{2}=p+\frac{0.4}{100}p=1.004p \, ;T_{2}=\left(\right.T+1\left.\right)$
As $\frac{p_{2}}{p_{1}}=\frac{T_{2}}{T_{1}} \, \therefore \, \frac{1.004 p}{p}= \, \frac{T + 1}{T}=1+\frac{1}{T}$
Or $T=\frac{1}{0.004}=250 \, K$