Homework Assignment 4, due Oct 7, 2019

Consider a Stirling engine, composed of four steps (all reversible)
  1. N moles of a monatomic ideal gas at high temperature Th expands isothermally from volume V1 to V2, where V2 > V1.

  2. The gas then is put in contact with a reservoir at temperature Tl, where Tl < Th. The gas is thus cooled at constant volume to temperature Tl.

  3. The gas is then compressed, isothermally, to volume V1.

  4. In the fourth step, the gas is put in contact with a reservoir at temperature Th. This heats the gas at constant volume to temperature Th. Thus, after four steps, the gas is returned to its initial state.
Answer the following questions:
  1. Sketch the four steps of the Sterling engine on a P, V plot (an isotherm plot). See the demonstration in the Wolfram Demonstration project.

  2. Determine, the total work w and the total heat q for the complete cycle as a function of the two temperatures, the two volumes, and N.

  3. The engine absorbs heat and produces work. A common defenition of the efficiency η of an engine is the ratio of the work done (|wtot|) divided by the heat in the high temperature step (q1). What is the efficiency of the reversible Stirling engine (again in terms of the temperatures, the volumes, and N ?)

  4. If Tl = 300 K, N = 0.2, V1 = 0.1 l, and V2 = 0.22 l, how high must the high-temperature Th be for the efficiency to be η = 0.5?

  5. Suppose the engine were irreversible, involving a single-step expansion and single-step contraction? Give an expression for the efficiency of the single-step Stirling engine?

  6. Estimate the number of moles, N, in the demonstration (The volume in the demonstration is measured in ml)

Also, Chapter 5 Problems: 1, 2, 5, 6, 10, 12, 23, 26, 27