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                                    An ideal gas at pressure` 2.5 xx 10^(5)` `pa` and temperture `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 peocess. Take `(gamma = 1.5)`. | 
                            
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Answer» `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`.  | 
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