If 5.40 kcal of heat is added to 1.00 kg of water at 100⁰C, how much steam at 100⁰C is produced? Show all calculations leading to an answer.
I can't figure this one out, can someone help me? Thank you!
Sure! To solve this problem, we need to use the concept of specific heat and the heat of vaporization.
First, let's calculate the heat required to raise the temperature of water at 100⁰C from its boiling point to steam at 100⁰C. The specific heat of water is 4.18 J/g·⁰C, and the heat of vaporization of water is 2260 J/g.
1. Calculate the heat required to raise the temperature of water:
Heat = mass × specific heat × change in temperature
= 1000 g × 4.18 J/g·⁰C × (100⁰C - 100⁰C)
= 0 J
As the temperature of the water remains constant at 100⁰C, there is no change in heat.
2. Calculate the heat required to convert water at 100⁰C to steam at 100⁰C:
Heat = mass × heat of vaporization
= 1000 g × 2260 J/g
= 2260000 J
Now, convert the heat into kilocalories for easier comparison with the given value:
Heat = 2260000 J ÷ 4.18 J/cal ÷ 1000 cal/kcal
≈ 540 kcal
The heat required to produce the steam is 540 kcal, which is equivalent to the heat that was added to the water at 100⁰C. Therefore, the 5.40 kcal of heat added to the water is not sufficient to produce steam.
To summarize, with the given conditions, it is not possible to produce any steam at 100⁰C since the heat provided is insufficient.