Question

If the pressure of a gas contained in a closed vessel increases by $x$ % when heated by $1^{\circ}C$, its initial temperature is

• A. $100/x\,Kelvin$
• B. $100/x\,Celsius$
• C. $\frac{x+100}{x}Kelvin$
• D. $\frac{x+100}{x}Celsius$

Answer 1

Answer: (A)

$100/x\,Kelvin$

Answer 2

Let the initial pressure and temperature be $P$ and $T$. From Ideal Gas Law, $\begin{array}{l} P \propto T \\\ \Longrightarrow \frac{\left(1+\frac{ x }{100}\right) P }{ P }=\frac{ T +1}{ T } \\\ \Longrightarrow T =\frac{100}{ x } K \end{array}$