A certain humidifier operates by raising water to the boiling point and then evaporating it.Every minute 30 g of water at 20°C are added to replace the 30 g that are evaporated.The heat of fusion of water is 333 kJ/kg, the heat of vaporization is 2256 kJ/kg, and the specific heat is 4190 J/kg How many joules of energy per minute does this humidifier require?

Question

A certain humidifier operates by raising water to the boiling point and then evaporating it.Every minute 30 g of water at 20°C are added to replace the 30 g that are evaporated.The heat of fusion of water is 333 kJ/kg, the heat of vaporization is 2256 kJ/kg, and the specific heat is 4190 J/kg  How many joules of energy per minute does this humidifier require?

Quizplus · Accepted Answer

To calculate the energy required, we need to consider the energy to heat the water from 20°C to 100°C and then the energy to vaporize it. The energy to heat the water is calculated using the specific heat formula: Q = mcΔT = 0.03 kg * 4190 J/kg°C * (100°C - 20°C) = 10,056 J. The energy to vaporize the water is: Q = mL = 0.03 kg * 2256 kJ/kg = 67,680 J. Adding these gives a total energy requirement of 77,736 J/min, which rounds to 77,700 J/min.

A Certain Humidifier Operates by Raising Water to the Boiling