Tessellate S.T.E.M.S - Physics - College - Set 2 - Problem 4

A heat conducting piston can freely move inside a closed thermally insulate cylinder with an ideal gas. In equilibrium the piston divides the cylinder into equal parts, the gas temperature being equal $T_0$ . The piston is slowly displaced. Then the gas temperature as a function of the ratio $\eta$ of the volumes of the greater and smaller sections is :

( The adiabatic exponent of the gas is equal to $\gamma$ .)

$(a)$ T = $T_0 \bigg[\dfrac {(\eta + 1)^2} {4\eta}\bigg]^\dfrac {\gamma - 1} {2}$

$(b)$ T = $T_0 \bigg[\dfrac {(\eta - 1)^2} {4\eta}\bigg]^\dfrac {\gamma - 1} {2}$

$(c)$ T = $T_0 \bigg[\dfrac {(\eta + 1)^4} {2\eta}\bigg]^\dfrac {\gamma + 1} {2}$

$(d)$ T = $T_0 \bigg[\dfrac {(\eta - 1)^2} {4\eta}\bigg]^\dfrac {\gamma + 1} {2}$

---

This problem is a part of Tessellate S.T.E.M.S.