50-g of hot water at 65 degree c is poured into a cavity in a very large block of ice at 0 degrees c. the final temperature of the water in the cavity is then 0 degrees c. what is the mass of the ice that melts?
solve using calories. show equations, units, and work.

Two kilograms of air within a piston–cylinder assembly executes a carnot power cycle with maximum and minimum temperatures of 800 k and 300 k, respectively. the heat transfer to the air during the isothermal expansion is 60 kj. at the end of the isothermal expansion the volume is 0.4 m3. assume the ideal gas model for the air. determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kj.