A 500 W electric heater is used to heat 1 kg of water without energy losses. The specific heat capacity of water is 4.2 kJ/kg K . What is the time taken to heat the water from 25 °C to 75 °C?
Correct answer: B. 420 seconds
- A. 7 seconds
- B. 420 seconds
- C. 8 minutes
- D. 420 minutes
Explanation
The formula for the amount of heat required to heat a substance is: Q = m × c × ΔTwhere Q is the amount of heat, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.In this case, we have:m = 1 kgc = 4.2 kJ/kg KΔT = 75°C - 25°C = 50°CSo the amount of heat required to heat 1 kg of water from 25°C to 75°C is:Q = m × c ×ΔTQ = 1 kg * 4.2 kJ/kg K * 50°CQ = 210 kJThe formula for power is:P = Q / twhere P is the power, Q is the amount of heat, and t is the time.In this case, we have:P = 500 WQ = 210 kJSo the time taken to heat the water from 25°C to 75°C is:t = Q / Pt = 210 kJ / 500 Wt = 420 secondsTherefore, the time taken to heat the water from 25°C to 75°C is 420 seconds or 7 minutes.
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