Question

A sample of a gas in a rigid container has an initial pressure of 1.049 kPa and an initial temperature of 7.39 K. The temperature is increased to 30.70 K. What is the new pressure?

Answer 1

Answer:- 4.36 kPa

Solution:- At constant volume, the pressure of the gas is directly proportional to the kelvin temperature.

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Where the subscripts 1 and 2 are representing initial and final quantities.

From given data:

$P_1$ = 1.049 kPa

$P_2$ = ?

$T_1$ = 7.39 K

$T_2$ = 30.70 K

For final pressure, the equation could also be rearranged as:

$P_2=\frac{P_1T_2}{T_1}$

Let's plug in the values in it:

$P_2=\frac{1.049kPa(30.70K)}{7.39K}$

$P_2$ = 4.36 kPa

So, the new pressure of the gas is 4.36 kPa.