Suppose you want to raise the temperature of a mass m of ice from T₀ < 0 C to T > 100 C. In this problem, represent the heat of fusion as L_f, the heat of vaporization as L_v, and the temperatures at which the phase changes occur as T_f and T_v.

part a. How much heat must be transferred for this to happen, including the energy needed for phase changes? Your answer should be in terms of the variables in the introduction and the specific heats of ice (c_i), water (c_w), and steam (c_s). The latent heats are L_f = 334 kJ/kg and L_v = 2256 kJ/kg

part b. How much heat, in kilocalories, must be transferred for this to happen to 0.22 kg of ice starting at a temperature of -20 C and ending at a temperature of 130 C?

part c. How much time, in seconds, is required, assuming a constant 20.0 kJ/s rate of heat transfer?