Answer:
The temperature must be changed to 4 times of the initial temperature so as to keep the pressure and the volume the same.
Explanation:
Pressure in the container is P and volume is V.
Temperature of the helium gas molecules =[tex] T_1[/tex]
Molecules helium gas = x
Moles of helium has = [tex]n_1= \frac{x}{N_A}[/tex]
PV = nRT (Ideal gas equation)
[tex]PV=n_1RT_1[/tex]...[1]
After removal of helium gas only a fourth of the gas molecules remains and pressure in the container and volume should remain same.
Molecules of helium left after removal = [tex]\frac{x}{4}[/tex]
Moles of helium has left after removal = [tex]n_2= \frac{x}{4\times N_A}[/tex]
[tex]PV=n_2RT_2[/tex]...[2]
[tex]n_1RT_1=n_2RT_2[/tex]
[tex]\frac{x}{N_A}\times T_1=\frac{x}{4\times N_A}\times T_2[/tex]
[tex]T_1=\frac{T_2}{4}[/tex]
[tex]T_2=4T_1[/tex]
The temperature must be changed to 4 times of the initial temperature so as to keep the pressure and the volume the same.
