To determine the heat lost to the tank holding the water and its surroundings, we need to calculate the amount of heat gained by the water and then subtract it from the total heat input provided by the 3kW immersion heater.
First, let's calculate the heat gained by the water using the formula:
Q = mcΔT
Where: Q = heat gained by the water (in Joules) m = mass of water (in kg) c = specific heat capacity of water (approximately 4,186 J/kg°C) ΔT = change in temperature (in °C)
m = 30 kg c = 4186 J/kg°C ΔT = (60°C - 10°C) = 50°C
Q = 30 kg * 4186 J/kg°C * 50°C Q ≈ 6,279,000 Joules
Next, let's calculate the heat input by the immersion heater in 40 minutes:
P = 3 kW (power of the immersion heater) t = 40 minutes = 40 * 60 seconds = 2400 seconds
Q_in = Pt
Q_in = 3 kW * 2400 seconds Q_in = 7,200,000 Joules
Now, we can calculate the heat lost to the tank and its surroundings:
Heat lost = Q_in - Q Heat lost = 7,200,000 Joules - 6,279,000 Joules Heat lost ≈ 921,000 Joules
Therefore, approximately 921,000 Joules of heat is lost to the tank holding the water and its surrounding during the heating process.