An ideal gas is enclosed in a closed container of `0.0083 m^3` at 300 K temperature and pressure of `1.6 xx 10^6` Pa. Find final temperature and pressure of the gas if `2.49 xx 10^4` J heat is supplied to the gas. Neglect expansion of the container. `R=8.3 "J mol"^(-1) K^(-1)`

Explanation

Using first law of thermodynamics
`DeltaQ=DeltaU+DeltaW` (volume expansion is neglected)
`therefore DeltaQ=DeltaU` (`because` volume constant `therefore DeltaW=0`)
`therefore DeltaQ=muC_VDeltaT` …(1)
Now using , `PV=muRT`
`P=1.6xx10^6` Pa
T=300 K
V=0.0083 `m^3`
`DeltaQ=2.49xx10^4` J
`R=8.3 "J-mol"^(-1) K^(-1)`
using `mu="PV"/"RT"`
`mu=(1.6xx10^6xx0.0083)/(8.3xx300)=16/3`...(2)
For ideal gas `C_V=3/2 R =3/2xx8.3`...(3)
Putting value of equation (2) and (3) in equation (1) and heat is to be given to gas is `DeltaQ=2.49xx10^4` J
`2.49xx10^4=16/3xx3/2xx8.3DeltaT`
`therefore DeltaT=(2.49xx10^4)/(8xx8.3)`
`DeltaT` = 375 K
`therefore` Final temperature =300+375
`Delta`T=675 K
For ideal gas `P prop T`
`therefore P_2/P_1 =T_2/T_1`
`therefore P_2=P_1 T_2/T_1=1.6xx10^6xx675/300`
`therefore P_2=3.6xx10^6` Pa