Question

On increasing the temperature of gas contained in closed vessel by $1^{o}C,$ the pressure increases by $0.4\%.$ The initial temperature of gas is:

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

Answer 1

The correct option is B $250$k

From the ideal gas equation,

PV =nRT

According to question,

New temperature, T' = T+1

New pressure, P' = P+0.4% of P

$\Rightarrow P^{\prime }=\frac{100.4P}{100}$

Therfore,equation becomes $\left(\frac{100.4P}{100}\right)V=nR(T+1)$

On dividing the two equations, we get

$\frac{100.4}{100}=\frac{T+1}{T}$

$\Rightarrow 1.004=1+\frac{1}{T}$

$\Rightarrow 1.004-1=\frac{1}{T}$

$\Rightarrow T=\frac{1}{0.004}$

Therefore, T = 250 K.

Hence,correct option is B.