An ideal gas at pressure `2.5 xx 10^(5)` `pa` and temperature `300k` occupies `100`cc. It is adiabatically compressed to half its original volume. Calculate (a) the final pressure, (b) the final temperature and ( c) the work done by the gas in the process. Take `(gamma = 1.5)`.

Explanation

`P_1=2.5xx10^(5) Pa`,
`T_1=300K`
`V_1 =100CC`,
(a) `P_1V_1^(gamma)=P_2V_2^(gamma)`
implies `2.5 xx 10^5 xx V^1.5=((V)/(2))^1.5 xx P_2`
implies `P_2=7.07xx10^5`
`=7.1xx10^5`
(b) `T_1V_1^(gamma-1)=T_2V_2^(gamma-1)`
implies`300xx(100)^(1.5-1)=T_2xx ((100)/(2))^(1.5-1)`
`=T_2xx(50)^(1.5-1)`
implies ` 300 xx 10 = T_2 xx 7.07`
`T_2 = 424.32 K=424K`.
(c) Work done by the gas in the process
`W=(mR)/(gamma-1)[T_2-T_1]`
`=(P_1V_1)/(gamma-1)[T_2-T_1]`
`=(2.5xx10)/(300xx0.5)xx124`
`=20.67=21J`.