Question

If the pressure of a gas contained in a closed vessel is increased by $0.4\%$ when heated by $1^{o}C$, its initial temperature must be:

• A. $250$ K
• B. ${250}^{o}C$
• C. $2500$ K
• D. ${25}^{o}C$

Answer 1

The correct option is A $250$ K

$PV=nRT$ ...(i)

$P(1+\frac{0.4}{100})V=nR(T+1)$ ....(ii)

On dividing equation (ii) by (i), we get:

$1+\frac{0.4}{100}=\frac{T+1}{T}=1+\frac{1}{T}$

$T=\frac{100}{0.4}=250K$

Hence, option A is correct.