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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About Thermal Equilibrium and Heat
Thermal equilibrium means that bodies in contact have the same temperature and no net heat flows between them. The topic distinguishes heat from temperature, uses the zeroth law of thermodynamics, and covers heat transfer, specific heat capacity, thermal expansion and the conditions for reaching equilibrium.
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