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Answer :
Final answer:
To calculate the time needed for the heating of the oil, we can use the formula: Q = mcΔT. We need to calculate the heat energy required to raise the temperature of 650 kg of oil from 22ºC to 220ºC, and then subtract the heat energy released when 650 kg of oil cools from 500ºC to 220ºC. The total heat energy supplied by the steam is 150 kW.
Explanation:
To calculate the time needed for the heating of the oil, we can use the formula: Q = mcΔT, where Q is the heat energy, m is the mass of the oil, c is the specific heat capacity of the oil, and ΔT is the change in temperature. We need to calculate the heat energy required to raise the temperature of 650 kg of oil from 22ºC to 220ºC, and then subtract the heat energy released when 650 kg of oil cools from 500ºC to 220ºC.
The heat energy required to raise the temperature of 650 kg of oil from 22ºC to 220ºC would be Q1 = mcΔT = 650 kg * 2.5 kJ/kg°C * (220°C - 22°C).
The heat energy released when 650 kg of oil cools from 500ºC to 220ºC would be Q2 = mcΔT = 650 kg * 2.5 kJ/kg°C * (500°C - 220°C).
The total heat energy supplied by the steam is 150 kW, which is equal to 150,000 J/s. We can divide the total heat energy supplied by the steam by the heat energy required to raise the temperature of 650 kg of oil from 22ºC to 220ºC minus the heat energy released when 650 kg of oil cools from 500ºC to 220ºC to find the time needed: t = (Q1 - Q2) / (150,000 J/s).
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