A cylindrical container $70$ cm long is separated into two compartments by a movable partition that is originally clamped in position $45$ cm from the right end. The right compartment is initially filled with one liter $($i$.$e$.,0\mathrm{.}001$m$^3)$ of helium gas at a pressure of $5$ x $106$ Pa$.$ The left compartment is filled with argon gas at $1$ x $106$ Pa of pressure. Both of these gasses may be considered ideal. The cylinder is submerged in $10$ liters of water and the entire system is initially at the uniform temperature of $270$ K$.$ When the piston is unclamped, a new equilibrium situation is ultimately reached with the piston in a new position. The entire system is thermally and mechanically isolated and y may ignore the heat capacities of the cylinder and the piston. What is the increase in the temperature of the water $($in K$)$ at the new equilibrium? The solution of the proble relies upon the fact that the pressures of the gasses must be the same at equilibrium.