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just needhelp with part a The Stirling engine (patented by Scottish clergyman Ro

ID: 1437015 • Letter: J

Question

just needhelp with part a

The Stirling engine (patented by Scottish clergyman Robert Stirling P in the year 1816) operates on a 4 step cycle (with 2 isothermal processes and 2 isovolumetric processes) as shown in the diagram. For this problem take T_H = 450 K, T_L = 300 K, V_b = 2Va, and assume the 'working substance' is one mole of a monatomic gas. Calculate the heat, Q, added or released during each of the 4 steps of the cycle. Q_ab = ? Q_bc = ? Q_cd = ? Q_da = ? Be sure to identify the correct sign of Q for each step. How much work is done by the engine during one complete cycle? What is the efficiency of a Stirling engine running on this cycle?

Explanation / Answer

a)

QQab = 2.303*n*RTH*log(Vb/Va) = 2.303*1*8.314*450*log2 = 2593.7 J


Qbc = n*CV*dT = n*R*dT/(gamma-1) = 1*8.314*(300-450)/(1.67-1) = -1861.34 J


Qcd = 2.303*n*RTL*log(Vd/Vc) = 2.303*1*8.314*300*log(1/2) = -1729.15 J

Qda = n*CV*dT = n*R*dT/(gamma-1) = 1*8.314*(450-300)/(1.67-1) = 1861.34 J
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b)

Wab = 2.303*n*RTH*log(Vb/Va) = 2.303*1*8.314*450*log2 = 2593.7 J

Wbc = 0



Wcd = 2.303*n*RTL*log(Vd/Vc) = 2.303*1*8.314*300*log(1/2) = -1729.15 J

Wda = 0


_____________

c)


Q = 2593.7-1861.34-1729.15+1861.34 = 864.55 J


W = 2593.7 - 1729.15 = 864.55

efficiency = w/Q = 864.55 /864.55 = 1