A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas , with specific heat at constant volume, `C_v=2R`. Here, R is the gas constant. Initially, each side has a volume `V_0` and temperature `T_0`. The left side has an electric heater, which is turned on at very low power to transfer heat `Q` to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to `V_0/2` . Consequently, the gas temperature on the left and the right sides become `T_L` and `T_R`, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition.
Value of `T_R/T_0`