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.

A thermally insulated vessel is divided in to two parts by a heat insu

1.	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» SOLUTION : `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`