An ideal gas expands from `100 cm^(3) to 200 cm^(3)` at a constant pressure of `2.0 xx 10^(5)` when `50 J` of heat is supplied to it. Calculate (a) the change in internal energy of the gas , (b) the number of moles in the gas if the initial temperature is 300K , (C ) the molar heat capacity `C_P` at constant pressure and (d) the molar heat capacity `C_v` at constant volume

Explanation

`V_1 =100 cm^(3)`, `V_2 =200 cm^(3)`,
`P=2xx10^(5) Pa` `dQ =50 J`
(a) `dQ = dU + dW`
implies `50 = dU + 2xx 10^(5)`
`(200-100)xx 10^(-6)`
implies `50 =dU + 2 xx 10`
implies `dU=30J`.
(b) `30 =n xx 3/2xx8.3 xx300`
[`U=3/2nRT` for monoatomic]
implies `n=(2)/(83xx3) = 2/249 = 0.008`
(c) `dU =nC_vdT`
implies `C_v =(dU)/(ndT)=(30)/(0.008xx300)=12.5`
`C_p =C_v +R =12.5 +8.3 =20.8`
(d) `C_v=12.5`