Helium is contained in a closed vessel with a volume of 2 liters at a temperature of `20^(@)C` and a pressure of `10^(5)N//m^(2)`.
a. What amount oif heat should be impated to the helium to increase its temperature to `100^(@)C`?
(ii) What will be the r.m.s velocity of its molecules be at the new temperature?
c. What will be the pressure be?
d. What is the density of the helium?

Explanation

Initial pressure `=10^(5)N//m^(2)`
Initial volume =2lt `=2xx1000` cc. `=0.002 m^(3)`
Initial temperature =293 K
As the vessel is closed, the process is a constant volume process.
Final temperature `=100^(@)C=373K`
Number of moles `=(10^(5)xx0.002)/(8.314xx293)=0.0821` moles
Specific heat at constant volume `C_(v)=(3R)/2=12.4` J/mole/K
a. Hence heat to be added `=(0.0821)(12.47)(80)=81.97J`
b. MOlecular weight of Helium `M=4xx10^(-3)kg`
`v_(rms)=sqrt((3RT)/M)=1525` m/s
c> `(P_(1))/(T_(1))=(P_(2))/(T_(2))implies(P_(2))/373=(10^(5))/293N//M^(2)`
`impliesP_(2)=1.27xx10^(5)N//m^(2)`
d `PV=m/M RT`
`implies(PM)/(Rt)=rho=0.164kg//m^(3)`