Question

A gas at the temperature $250\mathrm{K}$ is contained in a closed vessel. If the gas is heated through $1\mathrm{K}$, then percentage increase in its pressure will be

• A. $0.4%$
• B. $0.2%$
• C. $0.1%$
• D. $0.8%$

Hint:

For constant volume, $\frac{\Delta P}{P} = \frac{\Delta T}{T}$.

Answer 1

The Correct Option is A

To find the percentage increase in pressure when a gas at 250 K is heated through 1 K, we will use the Ideal Gas Law and the concept of proportional change in pressure relative to temperature for a gas in a closed vessel.

The Ideal Gas Law is given by:

\(PV = nRT\)

Where:

• \(P\) is the pressure
• \(V\) is the volume
• \(n\) is the number of moles of gas
• \(R\) is the universal gas constant
• \(T\) is the temperature in Kelvin

 

Since the gas is contained in a closed vessel, \(V\) and \(n\) are constant. Therefore, we can say:

\(\frac{P_1}{T_1} = \frac{P_2}{T_2}\)

Where:

• \(P_1\) is the initial pressure
• \(T_1 = 250\ \mathrm{K}\) is the initial temperature
• \(P_2\) is the final pressure
• \(T_2 = 251\ \mathrm{K}\) is the final temperature

 

Rearranging the equation for \(P_2\), we have:

\(P_2 = P_1 \times \frac{T_2}{T_1}\)

Let's calculate the fractional change in pressure:

\(\frac{P_2 - P_1}{P_1} = \frac{T_2 - T_1}{T_1}\)

\(\frac{P_2 - P_1}{P_1} = \frac{1}{250}\)

The percentage increase in pressure is then given by multiplying by 100:

\(Percentage\ Increase = \left(\frac{1}{250}\right) \times 100 = 0.4\%\)

Therefore, the correct answer is 0.4%.