Question

When the temperature of a gas in a vessel is increased by 1${}^0$ C then its pressure is increased by 0.5%. The initial temperature is

• A. 100 K
• B. 200 K
• C. 273 K
• D. 300 k

Answer 1

The correct option is B 200 K

As the process takes place in a vessel the volume remains constant. Thus using Gay-Lussac's law we have $\frac{P}{T}=constant$.
Pressure is increased by 0.5% Thus we get the final pressure as $P+\frac{0.5}{100}P=\frac{P}{200}$.Thus the final pressure is $P+\frac{P}{200}$Thus we get
$\frac{P}{T}=\frac{P(1+\frac{1}{200})}{T+1}$
or
$\frac{T}{T+1}=1+\frac{1}{200}$
or
$T=200K$