Question

A fire breaks out and increases the Kelvin temperature of a cylinder of compressed gas by a factor of 2.4. What is the final pressure of the gas relative to its initial pressure?

Answer 1

Answer:

P(final) is 2.4 times P(initial).

Explanation:

Here we can assume that the cylinder did not break and it's volume and number of moles of gas present in the cylinder remains constant.

Given the temperature increases by a factor of 2.4. Let us assume that the initial temperature be $T_{1}$ and the final temperature be $T_{2}$.

Given that $T_{2}=2.4\times T_{1}$

Now we know the ideal gas equation is PV=nRT

here V=constant , n=constant , R=gas constant(which is constant).

$\frac{P}{T}=constant$

$\frac{P_{1} }{T_{1}}=\frac{P_{2} }{T_{2} }$

$P_{2}=(\frac{T_{2} }{T_{1} } )P_{1}$

$P_{2}=(\frac{2.4T_{1} }{T_{1} } )P_{1}$

$P_{2}=2.4\times P_{1}$