A cylindrical container

$7$

$0$

$$cm long is separated into two compartments by a movable partition that is originally clamped in position

$4$

$5$

$$cm from the right end. The right compartment is initially filled with one liter

$($

i

$.$

e

$.$

$,$

$0$

$.$

$0$

$0$

$1$

m

$3$

$)$

$$of helium gas at a pressure of

$5$

$\backslash$times

$1$

$0$

$6$

P

a

$.$

$$The left compartment is filled with argon gas at

$1$

$\backslash$times

$1$

$0$

$6$

P

a

$$of pressure. Both of these gasses may be considered ideal. The cylinder is submerged in

$1$

$0$

$$liters of water and the entire system is initially at the uniform temperature of

$2$

$7$

$0$

$$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 you 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 problem relies upon the fact that the pressures of the gasses must be the same at equilibrium.