A cylindrical container having nonconducting walls is partitioned in two equal parts such that the volume of the each parts is equal to` V_(0).` A movable nonconducting piston is kept between the two parts. Gas on left is slowly heated so that the gas on right is compressed upto volume `(V_(0))/(8).` Find pressure and temperature on both sides if initial pressure and temperature, were `P _(0) and T_(0)` respectively. Also find heat given by the heater to the gas. (number of moles in each part is n)

Explanation

Since the process on right is adiabatic therefore
`PV^(gamma)=` constant.
`implies P_(0) V _(0) ^(gamma) = P _("final") ( V _(0) // 8) ^(gamma)`
`implies P_("total") =32 P _(0)`
`T _(0) V _(0)^(gamma -1) =T_("final") (V_(0) //8) ^(gamma -1)`
`implies (P_(0)V _(0))/(T_(0)) = (P_("final") V _(1))/(T _("final")) implies T _("final") = 60 T_(0)`
`Delta Q = Delta u + Delta w`
`Delta Q =n ( 5R)/(2) ( 60T_(0) -T_(0)) + n (3R)/(2) (4 T_(0) -T_(0))`
`Delta Q = (5nR)/(2 ) xx 59T_(0) + (3nR)/(2) xx 3T _(0)`