Thermodynamics - Using steam tables to find unknowns

[mandangalo]

Homework Statement

Determine the temperature, quality, and internal energy of 5 kg of (pure) water in a rigid container of volume 1 m³ at a pressure of 2 bar.

Homework Equations

PV = nRT (maybe?)
quality = n_v/(n_l + n_v) where l = number of moles in liquid phase and v = number of moles in vapor phase

The Attempt at a Solution

So far I have been able to determine that since P = 2 bars, it is also equal to 200 kPa.
V is also equal to 1000L.
5kg H₂O*(1000g/1kg)*(1 mol H₂O/18.01g H₂O)=277.53 moles H₂O.
Plugging this into the ideal gas equation, and rearranging to solve for T, I got this:
T = (200 kPa)(1000L)/(277.53 moles)(8.314 J*mol^-1*K^-1) = 86.68K = -186.47^oC

First off, are my calculations correct? If not, where did I go wrong?
Secondly, once temperature is correctly solved for, how do I use that information with steam tables to find out the internal energy and composition of water in the liquid and vapor phases? My textbook does not give any examples of how to calculate those.

 

[KataKoniK]

Your calculations for temperature seem to be correct. However, for the internal energy and quality, you will need to use the steam tables. These tables provide the thermodynamic properties of water at different temperatures and pressures. You can find these tables online or in a thermodynamics textbook.

To find the internal energy, you will need to use the specific enthalpy values from the steam tables. The specific enthalpy is the total energy of a substance per unit mass. For water, there will be different specific enthalpy values for the liquid and vapor phases at a given temperature and pressure. You can use the specific enthalpy values to calculate the internal energy of the water in the container.

To find the quality, you will need to use the saturation temperature and pressure values from the steam tables. The saturation temperature is the temperature at which water changes from liquid to vapor at a given pressure. The saturation pressure is the pressure at which water changes from liquid to vapor at a given temperature. Using these values, you can calculate the quality of the water using the equation you provided in the post.

Overall, to find the internal energy and quality of the water in the container, you will need to use the steam tables and the information you have already calculated for temperature and pressure. It may also be helpful to review the concepts of enthalpy and quality in thermodynamics to better understand these calculations.