The working fluid in an engine is N atoms of an ideal, monatomic gas. Once cycle

Question

The working fluid in an engine is N atoms of an ideal, monatomic gas. Once cycle of the engine is represented in Figure 22.23 in Lea and Burke.

Note: for parts a to f you are going to be finding the given quantities in terms of PA and VA (and for temperature calculations in terms of k and N, too). In the blanks for these four parts, input only the numerical coefficient for each solution (i.e. not the PA and VA).

(a) From A to B, the gas is compressed at constant pressure until its volume is VB=VA/8. Compute the gas temperatures at A and B in terms of only PA, VA, N, and k and insert the numerical coefficients you find when writing the temperatures in this form. TA's coefficient: TB's coefficient:

(b) Compute the work done by the gas along AB in terms of PA and VA and enter the numerical coefficient here:
(c) Compute the heat input to the gas on the leg AB in terms of PA and VA and enter the numerical coefficient here:
(d) On the leg BC, the gas is heated at constant volume. If the pressure at C is PC=32PB, what is the temperature in terms of only PA, VA, N, and k. Input the numerical coefficient here:
(e) What is the heat absorbed by the gas along path BC in terms of PA and VA. Give the numerical coefficient here:
(f) The gas expands adiabatically from C to A. Compute the work done by the gas on this leg in terms of PA and VA. Input the numerical coefficient here:
(g) What is the efficiency of this engine?
(h) Prove that the given conditions are such that an adiabatic expansion from state C actually returns to state A

please show all steps and details if possible

Explanation / Answer

Part a) PV = NkT TA = PV/Nk, TB = PV/8Nk

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