Calculate the change in internal energy of 2kg of water at 90 degree celcius when it is changed to $3.30m^{3}$ of steam at $100 ^{o}$C. The whole process occurs at atmospheric pressure. The latent heat of vaporization of water is $2.26\times10^{6}$ J/kg.
ANSWER
Answer
To calculate the change in internal energy of water when it changes from 90°C to steam at 100°C, we need to consider two steps of the process:
1. Heating the water from 90°C to its boiling point (100°C) at constant pressure.
2. Converting the water at its boiling point to steam at the same temperature and pressure.
Let's calculate the change in internal energy for each step:
Step 1: Heating the water from 90°C to 100°C
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The specific heat capacity of water is approximately 4,186 J/kg°C.
The mass of water is 2 kg.
The change in internal energy can be calculated using the formula:
ΔU = m * c * ΔT
Where:
ΔU is the change in internal energy,
m is the mass of the substance,
c is the specific heat capacity of the substance,
ΔT is the change in temperature.
Using the formula, we can calculate the change in internal energy for this step:
ΔU1 = 2 kg * 4,186 J/kg°C * (100°C - 90°C)
Step 2: Converting the water to steam at 100°C
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The latent heat of vaporization of water is given as 2.26 × 10^6 J/kg.
The mass of water is 2 kg.
The change in internal energy during the phase change can be calculated by multiplying the mass of water with the latent heat of vaporization:
ΔU2 = m * L
Where:
ΔU2 is the change in internal energy during the phase change,
L is the latent heat of vaporization,
m is the mass of the substance.
Using the formula, we can calculate the change in internal energy for this step:
ΔU2 = 2 kg * 2.26 × 10^6 J/kg
Total change in internal energy:
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To find the total change in internal energy, we sum up the change in internal energy for each step:
Total ΔU = ΔU1 + ΔU2
Once you have calculated ΔU1 and ΔU2 using the formulas and given values, you can substitute them into the equation to find the total change in internal energy.