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A sample of diatomic gas with y=1.5 is c...

A sample of diatomic gas with y=1.5 is compressed from a volume of 1600 cc to 400 cc adiabatically. The initial pressure of gas was `1.5xx10^5` Pa.Find the final pressure and work done by the gas in the process.

Text Solution

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We know in an adiabatic process, pressure and volume of gas of its different sates are related as
`P_1V_1^gamma=P_2V_2^gamma`
or `P_2=(V_1/V_2)^(gamma).P_1`
`=(1600/400)^(1.5)xx1.5xx10^5`
`=(4)^(1.5)xx1.5xx10^5`
`=1.2xx10^6` Pa
For an adiabatic process work done by a gas is given as
`W=(P_1V_1-P_2V_2)/(gamma_1)`
`=(1.5xx10^5xx1600xx10^(-6)-1.2xx10^6xx400xx10^(-6))/(1.5-1)`
`=(240-480)/0.5`=-480 J
Here work done by gas comes out a negative value thus we can state that as gas is being compressed , work is done on the gas and so work done by gas is -480 J.
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