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 compression is isothermal. (gamma=5//3)

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 compression is isothermal. (gamma=5//3)
Answer» Solution : During an adiabatic process `T_(1)V_(1)=T_(2)V_(2)` Here, `T_(1)=273K, V_(2)=(V_(1))/(2), gamma=(5)/(3)` `:.273 xx V_(1)^((5)/(3)-1)=T_(2)((V_(1))/(2))^((5)/(3)-1)` `T_(2)=(2)^(2//3) xx 273 =431.6K` 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)` `=8.34 xx 3)/(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=8.314J mol^(-1)K^(-1) rArr (V_(2))/(V_(1)) =(1)/(2)=0.5` `:.W=(2.306xx8.314xx273 log_(10) (0.5))/(22.4) rArr W= -70J`