QQuestionPhysics
QuestionPhysics
"If you add 1.33 MJ of heat to 500 g of water at 50°C in a sealed container, what is the final temperature of the steam?
The latent heat of vaporization of water is 22.6×10
5
J/kg.
The specific heat of steam is 2010 J/kg K.
The specific heat of water is 4186 J/kg K.
A) 195°C
B) 123°C
C) 112°C
D) 100°C
E) 147°C"
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Answer
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Step 1: Calculate the amount of heat needed to vaporize the water.
q = 0.5 \ \text{kg} \times 22.6 \times 10^5 \ \text{J/kg} = 11300000 \ \text{J} = 11.3 \ \text{MJ}
The amount of heat required to change a certain amount of substance from a liquid to a gas at constant temperature is given by the formula: In this case, we are given that 1.33 MJ of heat is added to 500 g of water. We need to find out how much of this heat is used to vaporize the water. First, let's convert the mass of water from grams to kilograms: Now, we can calculate the amount of heat needed to vaporize the water:
Step 2: Calculate the final temperature of the steam.
T_{\text{final}} = T_{\text{initial}} + \Delta T = 50°C + 9615.4°C = 9665.4°C
After vaporizing the water, there is still some heat left. This heat will increase the temperature of the steam. The amount of heat needed to raise the temperature of a substance is given by the formula: In this case, the remaining heat is: Since the change in temperature is positive when the final temperature is higher than the initial temperature, we should take the absolute value of the remaining heat: The mass of the steam is equal to the mass of the water, which is 0.5 kg. The specific heat of steam is 2010 J/kg K. We can now calculate the change in temperature: The initial temperature of the water is 50°C, so the final temperature of the steam is: However, this temperature is much higher than the boiling point of water, which means that some of the assumptions made in the calculation are not valid. In particular, the specific heat of steam is not constant at high temperatures. Therefore, we need to use a more accurate value for the specific heat of steam at high temperatures. According to the steam tables, the specific heat of steam at 100°C is about 2080 J/kg K. Using this value, we can recalculate the change in temperature: The final temperature of the steam is: This temperature is still higher than the boiling point of water, but it is closer to the actual final temperature.
Final Answer
The final temperature of the steam is not one of the given options. However, if we use a more accurate value for the specific heat of steam at high temperatures, we get a final temperature of about 9665.4°C. This temperature is much higher than the boiling point of water, but it is the best estimate based on the given information.
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