A thermally insulated vessel is divided in to two parts by a heat insulating piston which can move in the vessel without the friction. The left part of the vessel contains one mole of an ideal monatomic gas, & the right part is empty. The piston is connected to the right wall of the vessel through a spring whose length in free state is equal to the length of the vessel as shown in the figure. Determine the heat capacity C of the system, neglecting the heat capacity of the vessel, piston and spring.

Answer

C=2R

Explanation

`C=C_(v)+(pdv)/(ndT)`
`C=(3R)/(2)+(pdv)/(ndT)`
`PV=RT`
`P(Ax)=RT " "PA=kx`
`rArrP=(RT)/(Ax)rArrP=(kx)/(A)`
`(kx)/(A)=(RT)/(Ax)kx^(2)=RT`
`2kx dx=RdT`
`dv=Adx`
`rArr(P(Adx))/(2kxdx)xxR`
`thereforePA=kx`
`rArr(Pdv)/(ndT)=(R)/(2)`
`C=(3R)/(2)+(R)/(2)=2R`