Consider a mass of gasoline m=350 g which is burnt to heat 4kg of ice initially at -30°C under atmospheric pressure. What is the final temperature of the obtained steam?
Question
Consider a mass of gasoline m=350 g which is burnt to heat 4kg of ice initially at -30°C under atmospheric pressure. What is the final temperature of the obtained steam?
Solution
To solve this problem, we need to consider the energy conservation principle. The energy released by burning gasoline is used to heat the ice and turn it into steam.
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First, we need to calculate the energy released by burning gasoline. The heat of combustion of gasoline is about 47 kJ/g. So, the energy released is E1 = m * Hc = 350g * 47 kJ/g = 16550 kJ.
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Then, we calculate the energy needed to heat the ice from -30°C to 0°C. The specific heat of ice is about 2.1 J/g°C. So, the energy needed is E2 = m * c * ΔT = 4000g * 2.1 J/g°C * 30°C = 252 kJ.
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Next, we calculate the energy needed to melt the ice at 0°C to water at 0°C. The heat of fusion of ice is about 334 J/g. So, the energy needed is E3 = m * Hf = 4000g * 334 J/g = 1336 kJ.
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Then, we calculate the energy needed to heat the water from 0°C to 100°C. The specific heat of water is about 4.18 J/g°C. So, the energy needed is E4 = m * c * ΔT = 4000g * 4.18 J/g°C * 100°C = 1672 kJ.
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Next, we calculate the energy needed to turn the water at 100°C into steam at 100°C. The heat of vaporization of water is about 2260 J/g. So, the energy needed is E5 = m * Hv = 4000g * 2260 J/g = 9040 kJ.
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Finally, we add up all the energy needed to heat the ice and turn it into steam, E = E2 + E3 + E4 + E5 = 252 kJ + 1336 kJ + 1672 kJ + 9040 kJ = 12300 kJ.
Since the energy released by burning gasoline is greater than the energy needed to heat the ice and turn it into steam, the final temperature of the obtained steam will be 100°C.
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