PHYSICS $2$: PLEASE SHOW HOW TO GET ANSWERS, PART A $(95\mathrm{.}9)$ AND B $(17\mathrm{.}2)$ ARE CORRECT, AND THE TEACHER SAID PART C THE ANSWER IS ABOUT $324\mathrm{.}7$K$.$ One mole of helium gas is injected into each side of a slidable, airtight lead piston that separates two chambers of a sealed cylinder. The outside of the cylinder is insulated everywhere except where noted below. The cylinder and piston have lengths and crosssectional area labeled in the diagram. The helium in the left chamber is heated from outside at a rate of $450$ W $,$ and the helium in the other chamber expels heat into a cool region. The full system eventually comes to steady$-$state. When it reaches steady state, the force needed to hold on the end cap is measured to be $18,000$N$,$ and the piston has slid to an equilibrium point that is a distance x from the left end.

Assume helium behaves as an ideal gas, and that heat transfer through the container walls is instantaneous $($but not through the lead piston$).$ The thermal conductivity of lead is $35$W$//$m$*$K$.$ The force holding the cap accounts for all forces on it$,$ including atmospheric pressure.

:$\mathrm{.}95\mathrm{.}9$K

a$.$ Find the temperature difference of the two chambers.

b$.$ Find the distance x$.$

c$.$ Find the temperature of the lead piston at its center.

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K