An ideal gas has a specific heat at constant pressure `C_P=(5R)/2`. The gas is kept in a closed vessel of volume `0.0083m^3`, at a temperature of 300K and a pressure of `1.6xx10^6 N//m^2`. An amount of `2.49xx10^4` Joules of heat energy is supplied to the gas. Calculate the final temperature and pressure of the gas.

Answer

A, B, C

Explanation

We know that `PV=nRT`
`:. n=(PV)/(RT)=(1.6xx10^6xx0.0083)/(8.3xx300)=16/3=5.33 moles`
`C_p=(5R)/2 rArr C_v=(3R)/2`
When `2.49xx10^4J` of heat energy is supplied at constant
volume then we can use the following relationship to find
change in temperature.
`Q=nC_vDeltaT`
`:. DeltaT=Q/(nC_v)=(2.49xx10^4)/(5.33xx3/2xx8.3)=375K`
Therefore, the final temperature
`=300+375=675K`
Applying Gay Lussac's Law, to find pressure
`(P_1)/(T_1)=(P_2)/(T_2)`
`rArr P_2=(P_1T_1)/(T_1)=(1.6xx10^6xx675)/300=3.6xx10^6 Nm^-2`