Question

Chuck Norris is wrastlin’ a polar bear in the arctic. It is currently negative 20 degrees Celsius at the North Pole, so Chuck decides he needs to increase the temperature of his surroundings in order to gain an advantage. He wants to heat up 85 kilograms of ice at negative 20 degrees Celsius until it becomes 85 kilograms of steam at 120 degrees Celsius. How much energy does this require?

Answer 1

Mass of ice = m = 85 kg

Initial temperature of ice = T₁ = -20 ^oC

Melting point of ice = T₂ = 0 ^oC

Boiling point of water = T₃ = 100 ^oC

Final temperature of steam = T₄ = 120 ^oC

Specific heat of ice = C_i = 2.108 kJ/(kg.K)

Specific heat of water = C_w = 4.186 kJ/(kg.K)

Specific heat of steam = C_s = 1.996 kJ/(kg.K)

Latent heat of ice = L_i = 334 kJ/kg

Latent heat of water = L_w = 2260 kJ/kg

Energy required = H

H = mC_i(T₂ - T₁) + mL_i + mC_w(T₃ - T₂) + mL_w + mC_s(T₄ - T₃)

H = (85)(2.108)(0 - (-20)) + (85)(334) + (85)(4.186)(100 - 0) + (85)(2260) + (85)(1.996)(120 - 100)

H = 263047.8 kJ

Energy required to heat up 85 kg of ice at -20^oC to 85 kg of steam at 120^oC = 263047.8 kJ