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An ideal gas has a molar heat capacity a...

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.

Text Solution

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As here volume of gas remains constant, we have
`(Delta Q)_(v) = mu C_(v) Delta T`
Here, `C_(v) = C_(P) - R (5//2) R - R = (3//2) R`
`mu = (PV)/(RT) = (1.5 xx 10^(6) xx 8.3 xx 10^(-3))/(8.3 xx 300) = (16)/(3)`
`2.49 xx 10^(4) = (16)/(3) xx (3)/(2) xx 8.3 Delta T`
i.e., `Delta T = 375` or `T_(2) - T_(1) = 375`, i.e., `T_(2) = (375 + 300)`
Now as for a given mass of an ideal gas at constant volume,
`P prop T`
`(P_(2)// P_(1)) = (T_(1) // T_(2))`
`P_(2) = (675)/(300) xx 1.6 xx 10^(6) = 3.6 xx 10^(6) N//m^(2)`
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