This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
To calculate the total heat required to evaporate the water, we need to consider two parts: 1. The sensible heat required to raise the temperature of the water from 15^ to its boiling point (100^). 2. The latent heat required to change the water from liquid to steam at its boiling point. Given values: Volume of water (V) = 15 litres Mass of water (m) = 15 kg (since 1 litre of water has a mass of 1 kg) Initial temperature (T_1) = 15^ Boiling temperature (T_2) = 100^ Specific Heat Capacity of water (c) = 4.18 kJ/kg^ Latent Heat of vaporization of steam (L_v) = 2256 kJ/kg Step 1: Calculate the change in temperature ( T). T = T_2 - T_1 = 100^ - 15^ = 85^ Step 2: Calculate the sensible heat (Q_s) required to raise the water temperature. The formula for sensible heat is Q_s = mc T. Q_s = (15 kg) × (4.18 kJ/kg^) × (85^) Q_s = 6300.9 kJ Step 3: Calculate the latent heat (Q_L) required to evaporate the water. The formula for latent heat of vaporization is Q_L = mL_v. Q_L = (15 kg) × (2256 kJ/kg) Q_L = 33840 kJ Step 4: Calculate the total heat (Q_total) required. Q_total = Q_s + Q_L Q_total = 6300.9 kJ + 33840 kJ Q_total = 40140.9 kJ The total heat required to evaporate all the water is 40140.9 kJ. What's next?