Question

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

Answer 1

Answer: (A)

$250K$

As the vessel is closed, so a volume of the container is constant.

P $\alpha$ T

where P = pressure

T= temperature

So,

$\frac{P_1}{P_2}=\frac{P_1}{P_2}$

now pressure in increased by 0.4%

$P_2=1.004P_1$

let $T_2=T_1+1$

$\frac{P_1\times V_1}{T_2}=\frac{P_2\times V_2}{T_2}$

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

$T_1=\frac{P_1\times T_2}{P_2}$

$T_1=\frac{P_1\times (T_1+1)}{1.004\times P_2}$

$T_1=\frac{T_1+1}{1.004}$

$1.004\times T_1=T_1+1$

$0.004\times T_1=1$

$T_1=\frac{1}{0.004}$

$T_1=250K$