Question

The pressure of a gas filled in a closed vessel increases by 0.4%. When temperature is increases by 1${}^o$C the initial temperature of the gas is

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

Answer 1

The correct option is B 250 K

Since volume is constant i.e number of moles is constant.

$P_1$ and $T_1$ are the initial pressure and temperature.

According to the question,

$P_2=1.004P_1{T}_2=T_1+1$

$\therefore \frac{P_1}{T_1}=\frac{P_2}{T_2}=\frac{(1+0.004)P_1}{T_2}\Rightarrow T_2=1.004T_1=(T_1+1)$

$0.004T_1=1$

$\Rightarrow T_1=250K$

Hence, Option B is correct