Question

At constant volume, when the temperature of a gas increases by $1^{\circ }\text{C}$, its pressure increases by $0.4\%$. What is its initial temperature ?

• A. $250\text{K}$
• B. $125\text{K}$
• C. $195\text{K}$
• D. $329\text{K}$

Answer 1

The correct option is A $250\text{K}$

At a constant volume, Pressure $\propto$ Temperature
Thus, we can write that,
$\frac{P_1}{P_2}=\frac{T_1}{T_2}$
Given, Initial pressure $\left(P_1\right)=P$
Final pressure $\left(P_2\right)=P+\frac{0.4}{100}P$
Initial temperature $\left(T_1\right)=TK$
Final temperature $\left(T_2\right)=(T+1)K$ (Temperature change in degree scale is same as Temperature change in kelvin scale)
$\Rightarrow \frac{P}{P+\frac{0.4}{100}P}=\frac{T}{T+1}$
$\Rightarrow \frac{100}{100.4}=\frac{T}{T+1}$
$\Rightarrow T=250\text{K}$
Hence, option (a) is the correct answer.