Calculate the change in internal energy of 2kg of water at 90 degree Celsius when it is changed to
3.30m3
of steam at
100oC
. The whole process occurs at atmospheric pressure. The latent heat of vaporization of water is
2.26×106J/kg
To calculate the change in internal energy of water when it is changed to steam, we need to consider two steps: heating the water to its boiling point and then converting it to steam at the boiling point.
Step 1: Heating water to boiling point:
To heat water from 90°C to 100°C, we need to calculate the energy required using the specific heat capacity of water.
The specific heat capacity of water is 4.18 × 10^3 J/(kg·°C).
Formula:
Energy = mass × specific heat capacity × change in temperature
Given:
Mass of water (m) = 2 kg
Specific heat capacity of water (C) = 4.18 × 10^3 J/(kg·°C)
Change in temperature (ΔT) = (100°C - 90°C) = 10°C
Energy required to heat the water = 2 kg × 4.18 × 10^3 J/(kg·°C) × 10°C
Step 2: Convert water to steam:
To convert water to steam at its boiling point, we need to consider the latent heat of vaporization.
The latent heat of vaporization of water (L) = 2.26 × 10^6 J/kg.
Formula:
Energy = mass × latent heat of vaporization
Given:
Mass of water (m) = 2 kg
Latent heat of vaporization (L) = 2.26 × 10^6 J/kg
Energy required to convert water to steam = 2 kg × 2.26 × 10^6 J/kg
Total change in internal energy: The change in internal energy is the sum of the energy required for heating and converting the water.
Total change in internal energy = Energy required to heat the water + Energy required to convert water to steam
Now you can plug in the values and calculate the total change in internal energy.