A monoatomic ideal gas, initially at temperature is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature by releasing the piston suddenly. If are the lengths of the gas column before and after expansion respectively, then is given by
A Carnot engine, having an efficiency of as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is