There are two vessels. Each of them contains one moles of a monoatomic ideal gas. Initial volume of the gas in each vessel is `8.3 xx 10^(-3) m^(3) at 27^(@)C`. Equal amount of heat is supplied to each vessel. In one of the vessels, the volume of the gas is doubled without change in its internal energy, whereas the volume of the gas is held constant in the second vessel. The vessels are now connected to allow free mixing of the gas. Find the final temperature and pressure of the combined gas system.

Answer

`00369.31`

Explanation

For first vessel
`DeltaU=0`
`DeltaQ_(1)=DeltaW=nRTln((V_(f))/(V_(i)))=1.R.300.ln2`
`=(0.6931)xx300xxR=207.93R`
For second vessel `DeltaV=0`
`DeltaQ_(2)=DeltaU=nC_(v)Deltat=1 . 3/2 RDeltaT`
`DeltaQ_(1)=DeltaQ_(2)`
`207.93R= 3/2 RDeltaT`
`impliesDeltaT=138.62`
`T_(f)=300+138.62=438.62`
`U_("mix")=U_(1)+U_(2)`
`(n_(1)+n_(2))C_(V_("mix"))T_("mix")=_(1)C_(V_(1))T_(1)+n_(2)CV_(2)T_(2)`
`=T_("mix")=(T_(1)+T_(2))/(n_(1)+n_(2))=369.31K`