One mole of an ideal monoatomic gas occupies a volume of `1.0xx10^-2m^3` at a pressure of `2.0xx10^5N//m^2`.
(a) What is the temperature of tha gas?
(b) The gas undergoes an adiabatic compression until its volume is decreased to `5.0xx10^-3m^3`. What is the new gas temperature?
(c) How much work is done on the gas during the compression?
(d) What is the change in the intenal energy of the gas?

Answer

A, B, C, D

Explanation

(a) `T=(pV)/(nR)=((2xx10^5)(1.0xx10^-2))/((1)(8.31))`
`=240.7K`
(b) In adiabatic process,
`TV^(gamma-1)=` constant
`:.` `T_fV_f^(gamma-1)=T_iV_i^(gamma-1)`
`:.` `T_f=T_i((V_i)/(V_f))^(gamma-1)`
`=(240.7)[(1.0xx10^-2)/(5.0xx10^-3)]^(5//3-1)`
`~~383K`
(c) Work done on the gas `=DeltaU`
=`nC_(V)Detla T`
`=(1)(3/2R)(T_f-T_i)`
`=1.5xx8.31(383-240.7)`
`~~1770J`
(d) `DeltaU~~1770J`