A cooling system uses ice at 0^ C to absorb heat rejected by a machine operating at a constant power of 4.2 kW . The ice completely melts and leaves the system as water at 20^ C . The mass of ice consumed per second by the cooling system is ________ g . (Given: Latent heat of fusion of ice = 336 10^3 J kg ⁻¹ , Specific heat capacity of water = 4200 J kg ⁻¹ ^ C ⁻¹ )

Step-by-step solution

Let the mass of ice consumed per second be m (in kg). The heat absorbed per second by the ice is the sum of the heat required to melt the ice and the heat required to raise the temperature of the resulting water to 20^ C . Rate of heat absorption, P = m(L_f + c_w T) Given: P = 4.2 kW = 4200 J s ⁻¹ L_f = 336000 J kg ⁻¹ c_w = 4200 J kg ⁻¹ ^ C ⁻¹ T = 20 - 0 = 20^ C Substituting the values: 4200 = m(336000 + 4200 20) 4200 = m(336000 + 84000) 4200 = m(420000) m = 4200 420000 = 0.01 kg s ⁻¹ Converting to grams: m = 0.01