A cylinder with a piston contains 0.3 kg of water at 100 degrees C. What is the change in internal energy of the water when it is converted to steam at 100 degrees C at a constant pressure of 1 atm? The density of water is 1000 kg/m^3 and that of steam is 0.6 kg/m^3. The latent heat of vaporization of water is 2.26E+06 J/kg.
To find the change in internal energy of the water when it is converted to steam, we can use the following equation:
Change in Internal Energy = Mass of Water × Specific Heat Capacity × Change in Temperature + Mass of Water × Latent Heat of Vaporization
In this case, we need to determine the mass of water, so we can use the formula:
Mass = Density × Volume
The volume of water can be calculated using the formula:
Volume = Mass / Density
The initial and final volumes will be the same since the phase change occurs at constant pressure and temperature. So, we can calculate the volume of water and then use it to find the mass of water.
Given:
Density of water (ρ_water) = 1000 kg/m^3
Density of steam (ρ_steam) = 0.6 kg/m^3
Mass of water (m_water) = 0.3 kg
Latent heat of vaporization of water (L_vap) = 2.26E+06 J/kg
First, let's calculate the volume of water using its mass and density:
Volume = Mass / Density = 0.3 kg / 1000 kg/m^3 = 0.0003 m^3
Since the volume of water and steam is the same, the volume of steam is also 0.0003 m^3.
Next, we can calculate the change in internal energy using the formula mentioned earlier:
Change in Internal Energy = Mass of Water × Specific Heat Capacity × Change in Temperature + Mass of Water × Latent Heat of Vaporization
Since the phase change occurs at 100 degrees C (the boiling point of water), the change in temperature is 0.
Change in Internal Energy = Mass of Water × Latent Heat of Vaporization
Change in Internal Energy = m_water × L_vap
Change in Internal Energy = 0.3 kg × 2.26E+06 J/kg = 678,000 J
Therefore, the change in internal energy of the water when it is converted to steam is 678,000 Joules.