An ideal gas has a molar heat capacity at constant pressure of `Cp = 2.5 R`. The gas is kept in a closed vessel of volume `0.0083 m^(3)`, at a temperature of `300 K` and a pressure of `1.6 xx 10^(6) Nm^(-2)`. An amount `2.49 xx 10^(4) J` of heat energy is supplied to the gas. Calculate the final temperature and pressure of the gas.

Explanation

No. of moles of the gas `(n) = (PV)/(RT) = ( 1.6 xx 10^(6) xx 0.0083)/( 8.3 xx300) =5.33`
Given `C_(p) = ( 5)/(2) R`
`:. C_(v) = C_(p) -R = ( 5)/(2) R-R= (3)/(2) R=(3)/(2) xx 8.3 = 12.45 JK ^(-1) mol^(-1)`
Heat supplied at constant volume `= n xx C_(v) = DeltaT`
`:.2.49 xx 10^(4) = 5.33 xx 12.45 xx Delta T ` or `DeltaT = 375K`
`:. `Final temperature `= 300 + 375 K = 675K`