Calculate the change in internal energy of 2kg of water at 90 degree celcius when it is changed to 3:30m3 of steam at 100oC. The whole process occurs at atmospheric pressure. The latent heat of vaporization of wat
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To calculate the change in internal energy of water when it is converted into steam, we need to consider two steps: heating the water to its boiling point and then converting it into steam.
Step 1: Calculate the energy required to heat the water from 90°C to its boiling point (100°C).
The specific heat capacity of water is approximately 4.186 J/g°C.
First, we need to determine the mass of water. Given that the mass is 2 kg, we convert it to grams:
Mass of water = 2 kg * 1000 g/kg = 2000 g
Next, we calculate the energy required to heat the water using the formula:
Energy = Mass * Specific Heat Capacity * Temperature Change
Temperature change = Final Temperature – Initial Temperature
Temperature change = 100°C – 90°C = 10°C
Energy = 2000 g * 4.186 J/g°C * 10°C
Step 2: Calculate the energy required to convert the water at its boiling point into steam at the same temperature.
The latent heat of vaporization of water is the amount of energy required to convert one unit mass of water into steam without any change in temperature. For water, this value is approximately 2260 J/g.
Using the given volume of steam (3.30 m^3) at atmospheric pressure, we can calculate the mass of steam:
Mass of steam = Volume * Density
The density of steam at atmospheric pressure is approximately 0.6 g/L.
Density = 0.6 g/L = 0.6 g/1000 cm^3 = 0.6 g/(1000*1000) m^3
Mass of steam = 3.30 m^3 * 0.6 g/m^3
Finally, we calculate the energy required to convert the water into steam:
Energy = Mass of steam * Latent Heat of Vaporization
Now you can calculate the change in internal energy by adding the energies from Step 1 and Step 2.