If a monoatomic ideal gas of volume 1 litre at N.T.P is compressed adiabatically to half of its volume, find the work done on the gas. Also find the work done if the comression is isothermal.

If a monoatomic ideal gas of volume 1 litre at N.T.P is compressed adi

1.	If a monoatomic ideal gas of volume 1 litre at N.T.P is compressed adiabatically to half of its volume, find the work done on the gas. Also find the work done if the comression is isothermal.
Answer» Solution :i) During an adiabatic process `T_(1)V_(1)^(gamma-1) = T_(2)V_(2)^(gamma-1)` Here, `T_(1)=273K, V_(2)=V_(1)/2 , gamma=5/3` ` :. 273xxV_(1)^(5/3-1) = T_(2)[V_(1)/2]^(5/3-1)` `T_(2)= (2)^(2/3)xx273= 431.6 K` number of moles,` n=(1" LITRE")/(22.4 " litre")=1/22.4` Work DONE = `(nR)/(gamma-1) (T_(1)-T_(2))` ` = 8.314/(22.4[5/3-1])(273-431.6)=(8.34xx3)/(22.4xx2)(-158.6)=-89J` ii) Work done during isothermal compression is `W=2.3026nRT log_(10)[V_(2)/V_(1)]` n=number of moles = `1/22.4` , `T=273K, R =8.314 "J mol" ^(-1)K^(-1) RARR V_(2)/V_(1)=1/2=0.5` ` :. W= (2.3026xx8.314xx273 log_(10) (0.5))/22.4 = W= -70J`