Chemical Thermodynamics

3. A completely reversible heat pump produces heat at a rate of 300 kW to warm a house maintained at 25°C. The exterior air, which is at 9°C, serves as the source. Calculate the rate of entropy change of the two reservoirs and determine if this heat pump satisfies the second law of thermodynamics, according to the increase of entropy principle. [MO7]

2. Which fluid will have a more negative internal energy departure function: water at 375°C and 2.3 bar or water at 100°C and 1.6 bar? Explain.

3. (a) Use the steam tables to determine the fugacity of steam at 1.0 MPa and 850°C. (b) Calculate the fugacity if the pressure is increased to 100 MPa.

4. Diamond is denser than graphite. Sketch the chemical potentials of graphite and diamond as a function of pressure for a region over which a phase transition occurs. Explain the graph.

6. Water was subcooled to -37°C and then allowed to equilibrate adiabatically. Specify the final state of the system including temperature and amounts of each phase if more than one is present.

7. A fixed-volume container at 45°C contains 5 mol hexane liquid and 0.1 mol hexane vapor in equilibrium. An additional 0.2 mol of hexane vapor are added, while keeping the temperature constant. What happens to the pressure and the amount of liquid and vapor in the container? Why?

5. Use the Peng-Robinson equation of state spreadsheet to determine the fugacity of saturated liquid benzene at 410 K, and then use the Poynting method to determine the fugacity at 410 K for a pressure of 47MPa. Compare to the result obtained from the spreadsheet at this condition.

4.9 As shown in Fig. P4.9, river water used to irrigate a field is controlled by a gate. When the gate is raised, water flows steadily with a velocity of 75 ft/s through an opening 8 ft by 3 ft. If the gate is raised for 24 hours, determine the volume of water, in gallons, provided for irrigation. Assume the density of river water is 62.3 lb/ft³.

You will be calculating a number of carbon dioxide (CO₂) properties using the van der Waals (VDW) equation of state (EoS). For each calculation, compare your results with ones calculated using NIST's thermophysical property estimator: (webbook.nist.gov/chemistry/fluid) by plotting the NIST data on the same plot as the VDW calculations. A table of the CO₂ properties has been uploaded to Canvas. Perform all calculations from -55 °C to the critical point of CO₂ using step sizes no larger than 10 °C. Hint: Do NOT attempt to solve this problem by hand, use a computer tool (i.e., Matlab). Calculate and plot the vapor pressure (in atm) as a function of temperature as calculated with the VDW EOS. On a P vs. V diagram, plot the specific volume of the liquid and vapor phase (i.e., the 2-phase boundary). Use units of atm for pressure, L/mol for specific volume, and use a log-log plot. Using the Clapeyron equation, calculate and plot the ASvap and AHvap as a function of temperature using only data generated with the VDW EoS. Hint: numerically approximate dpap/dr. Which properties are accurately predicted by the VDW EoS? Which properties have the greatest difference with the NIST data?

4.6 WP Figure P4.6 shows a mixing tank initially containing 2000 lb of liquid water. The tank is fitted with two inlet pipes, one delivering hot water at a mass flow rate of 0.8 lb/s and the other delivering cold water at a mass flow rate of 1.2 lb/s. Water exits through a single exit pipe at a mass flow rate of 2.5 lb/s. Determine the amount of water, in lb, in the tank after one hour.