Homework 3

Problem 1

Consider a solar-pond power plant that operates on a simple ideal Rankine cycle with R134a as the working fluid. The refrigerant enters the turbine as a saturated vapor at 1.6 MPa and leaves at 0.7 MPa. The mass flow rate of the refrigerant is 6 kg/s. Show the cycle on a TS diagram with respect to the saturations lines. (You can either modify the provided codes to use “Hfc134a” instead of “Water”, or you can look up an existing diagram and draw on that.) Find the thermal efficiency and the power output of the plant.
–adapted from Cengel and Bowles “Thermodynamics” 3rd edition p. 597

Problem 2

Consider a mixture of CO$_2$/air. Find the work required per kg of CO$_2$ separated. Assume ambient conditions of 1 atm and 77 $^o$F. Assume steady state operation, and any heat transfer occurs at the ambient temperature. Take the CO$_2$ concentration to be 412 ppmv. Compare the work required to that for separating CO$2$ at a mole fraction of 10%, which is a concentration in a stoichiometric methane-air flame effluent (100000 ppmv). To compare the work in a meaningful way, take the ratio of the work for the low concentration to the work for the high concentration. Note, the entropy per mole of a mixture of ideal gases is given by $$s{mix} = \sum_ix_is_i^o - R\sum_ix_i\ln x_i$$ where $s_i^o$ is the entropy of the pure species at the given temperature and pressure.

Problem 3

Find an article online, or in a magazine, or in the technical literature describing an aspect of the impact of combustion on society. Write a one page paper (single spaced, 12 point font) on this article. Include in your writeup the title, author, and the basic idea of the article. You can include more than one source if desired. Possible ideas for discussion follow. What were the main conclusions? Do you agree with the main conclusions or aguments? Is there a consensus? What is the direct impact of combustion? Topics may include electric power generation, transportation, greenhouse gas emissions, pollutant emissions, home heating and cooking, etc. Your writing and style matters here, use a spell checker. Turn in your writup and a copy of the article, or a link to the online article.

Problem 4

Consider a fuel which is an equimolar mixture of propane (C$_3$H$_8$) and natural gas (CH$_4$). Write out the complete stoichiometric combustion reaction for this fuel burning with air and detremine the stoichiometric fuel-air ratio on a molar basis. Also, determine the molar air-fuel radio for combustion at an equivalence ratio, $\phi$, of 0.8.
–Turns “Combustion” 3rd edition, page 71.

Problem 5

Compare the adiabatic flame temperature for stoichiometric methane-air combustion to that for stoichiometric methane-oxygen combustion.

  • You can use the online combustion tool for this. Use an HP equilibrium.
  • Do the same thing for a UV equilibrium. So, you will be comparing temperatures under four conditions.
  • Report the four temperatures in both K and $^o$F.
  • For comparison, what is the temperature of the surface of the sun?
  • Is the temperature difference with air vs with oxygen as high as you thought it would be? How does the heat capacity of the products change with temperature? Will this have the effect of making the increase in temperature higher or lower?

Problem 6

For natural gas (methane) combustion, how much excess air (as a percentage of stoichiometric air) is needed to get 5% O$_2$ in products of complete combustion?