Question 13

Thermal equilibrium: same temperature T on both sides (piston conducting). Volumes equal (L/2 each). Left pressure: P_L = (3/2)RT/(AL/2) = 3RT/(AL) Right pressure: P_R = RT/(AL/2) = 2RT/(AL) So P_L = (3/2)P_R. Spring natural length 2L/5, compressed to L/2, so compression x = L/2 − 2L/5 = L/10. Spring is compressed and pushes the piston to the right with force kL/10. Piston equilibrium: P_L A + kL/10 = P_R A → (3/2)P_R A + kL/10 = P_R A → P_R A = −kL/5 Sign issue: spring compressed pushes rightward, left pressure larger also pushes right — inconsistent. So the spring must be stretched (attached at left wall, natural length 2L/5, current length L/2 means stretched by L/10, pulling the piston leftward): P_L A = P_R A + kL/10 → (1/2)P_R A = kL/10 → P_R = kL/(5A) α = 0.2

No written reasoning was returned for this item.

No written reasoning was returned for this item.