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 x 10^(6) Nm^(-2). An amount 2.49 x 10^(4) J of heat energy is supplied to the gas. calculate the final temperature and pressure of the gas.

Answer

`675 K , 3.6 xx 10^(6)N//m^(2)`

Explanation

Number of moles n=`(PV)/(RT) = ((1.6xx 10^(6))(0.0083))/((8.3)(300)) = (16)/(3)`
Heat is supplied at constant volume so `Q = nC_(V)DeltaT`
`implies T_(2) = T_(1) + (Q)/(nC_(V)) = 300 + (2.49 xx 10^(4))/(((16)/(3))((3R)/(2)))`
= `300+375 = 675K`
As `V` = constant So `(P_(2))/(P_(1)) = (T_(2))/(T_(1))`
`implies P_(2) = ((675)/(300))(1.6 xx 10^(6)) = 3.6 xx 10^(6)Nm^(-2)`