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.
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To solve this problem, we need to use the concept of specific heat and latent heat.
First, let's calculate the amount of heat needed to raise 1 kg of water from 100⁰C to its boiling point at 100⁰C.
The specific heat of water is 4.18 J/g·⁰C, which means it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1⁰C. Since we have 1 kg of water, which is equal to 1000 grams, we can calculate the energy required to raise the temperature of 1 kg of water from 100⁰C to its boiling point at 100⁰C.
Energy = Mass × Specific Heat × Temperature Difference
Energy = 1000 g × 4.18 J/g·⁰C × (100 - 100)⁰C
Energy = 0 J
As we can see, no additional energy is required to raise the temperature of water from 100⁰C to its boiling point at 100⁰C. This is because at its boiling point, the temperature of water does not increase further.
Next, let's calculate the amount of heat needed to convert 1 kg of water at 100⁰C to steam at the same temperature.
The latent heat of vaporization for water is 2260 J/g, which means it takes 2260 Joules of energy to convert 1 gram of water into steam at 100⁰C. Since we have 1 kg of water, which is equal to 1000 grams, we can calculate the energy required to convert 1 kg of water into steam at 100⁰C.
Energy = Mass × Latent Heat
Energy = 1000 g × 2260 J/g
Energy = 2,260,000 J
Therefore, to produce steam, we need a total of 2,260,000 Joules of energy.
Now let's calculate the amount of heat added to the system, given as 5.40 kcal.
1 kcal is equal to 4184 Joules, so 5.40 kcal is equal to 5.40 × 4184 = 22,609.6 Joules.
Since the amount of heat added to the system is less than the amount of energy required to convert 1 kg of water into steam, it is not possible to produce steam in this scenario.
In conclusion, no steam at 100⁰C is produced with the given conditions as the amount of heat added is insufficient to convert 1 kg of water into steam at 100⁰C.