You are trying to improve an engine that you are working on in your hobby shop. Currently, your engine is based upon the Stirling cycle shown in the figure on the left. You decide to modify the Stirling cycle in the following two ways:

1) The isothermal compression continues past volume V_a until the pressure reaches p_b.

2) The gas is then held at pressure p_b while it expands from V_e to V_a.

This gives you the "modified Stirling cycle", shown in the figure on the right.

The working gas in this engine is 1.00 mole of methane (CH₄), a polyatomic gas that translates and rotates but does not oscillate. The low temperature reservoir is at T_L = 300 K, and the high temperature reservoir is at T_H = 450 K. At point a, the methane has volume V_a = 2.5 x 10^-4 m³ (or one quarter of a liter) and is at pressure p_a = 9.98 x 10⁶ Pa. The volume of the methane at point d is V_d = 4V_a.

Answer the questions below. Report all of your answers to four significant figures.

(a) What are the pressure p_b and the volume V_e?

(b) If the methane does W_OS = 1.73 kJ of work during the original Stirling cycle, how much work WMS does the methane do during one cycle of the modified Stirling cycle?

(c) If Q_abc = 8.93 kJ of heat is added to the methane during process abc of the original Stirling cycle, how much heat Q_aeb is added during process aeb of the modified Stirling cycle?

(d) Compare the efficiency E(epsilon)_MS of the modified cycle to the efficiency E(epsilon)_OS of the original cycle. Does this modification of the Sterling cycle make financial sense in terms of energy costs? (For example, if E_MS > E_OS, is it appreciably larger?)