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An ideal gas has a specific heat at cons...

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.

Text Solution

Verified by Experts

The correct Answer is:
`675, 3.6 xx10^6`
Vessel is closed. Therefore, `Delta W =0` or `Delta Q =Delta U = nC_V DeltaT `
`Delta T = (Delta Q)/(nC_V) = (DeltaQ)/(((pV)/(RT))(C_P -R))= ((Delta Q)(RT))/(pV (C_p -R))`
Substituting the values, we have
`Delta T =((2.49 xx10^4)(300))/((1.6 xx10^6)(0.0083)(3//2)) = 375 " ":." "T_f = Delta T + T = 675 K`
Further at constant volume
`P_2/P_1 = T_2/T_2" ":." "P_2 = T_2/T_1 P_1 = (675/300) (1.6 xx10^6)" , "=3.6 xx10^6 "N/m"^2`
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