Final answer:
The final temperature can be found using the ideal gas law. The work done on the water can be calculated using the formula for work. The change in internal energy can be determined using the formula for change in internal energy. The thermodynamic process is isobaric.
Step-by-step explanation:
To find the final temperature of the water, we can use the ideal gas law.
Given:
- Mass of water (m) = 5 kg
- Pressure (P) = 5 bar = 5 x 10^5 Pa
- Initial temperature (T1) = 300°C = 573 K
Using the ideal gas law: PV = nRT
We know:
- V = mass/density = m/ρ = 5 kg/(1000 kg/m³) = 0.005 m³
- R = gas constant = 8.314 J/(mol·K)
Substituting the given values into the ideal gas law equation, we have:
5 x 10^5 Pa x 0.005 m³ = n x 8.314 J/(mol·K) x 573 K
Solving for n, the number of moles of water:
n = (5 x 10^5 Pa x 0.005 m³) / (8.314 J/(mol·K) x 573 K) = 0.0117 mol
Now, using the equation:
n = mass / molar mass of water (18.015 g/mol)
Solving for mass:
mass = n x molar mass = 0.0117 mol x 18.015 g/mol = 0.2112 g
Therefore, the final temperature of the water is 0.2112 g.
The work done on the water can be calculated using the equation:
Work = Pressure x Change in volume = P x (final volume - initial volume)
Since the pressure is constant, the work can be simplified to:
Work = P x Change in volume
Given:
- Initial volume (V1) = mass/density = 5 kg / (1000 kg/m³) = 0.005 m³
- Final volume (V2) = 2 x Initial volume = 2 x 0.005 m³ = 0.01 m³
Substituting the given values into the equation:
Work = 5 x 10^5 Pa x (0.01 m³ - 0.005 m³) = 2500 J
Therefore, the work done on the water is 2500 J.
The change in internal energy can be calculated using the equation:
Change in internal energy = Mass x Specific heat x Change in temperature
Given:
- Mass (m) = 5 kg
- Specific heat of water (C) = 4.184 J/(g·K)
- Change in temperature (ΔT) = Final temperature - Initial temperature
Substituting the given values into the equation:
Change in internal energy = 5 kg x 4.184 J/(g·K) x (final temperature - 300 K)
Therefore, to calculate the change in internal energy, we need to know the final temperature.
The type of thermodynamic process can be determined by analyzing the given information. In this case, the water is heated at constant pressure, which implies an isobaric process.