A heat engine containing an ideal gas has a reversible cycle which consists of 2

Question

A heat engine containing an ideal gas has a reversible cycle which consists of 2 constant volume segments with V = 1 l and V = 3 l and two constant pressure segments with P = 1 atm and P = 2 atm (see figure below). The temperature at point “c” is Tc = 273 K.

(a) Is the path of the cycle clockwise or counter-clockwise? Explain.

(b) How much work is done by the engine in one cycle?

(c) What is the efficiency of the engine? Notice that this is a reversible engine, so recall the efficiency of a Carnot engine and use the ideal gas law.

Explanation / Answer

b) Work done = Area under the graph = P*V = (2-1)atm*(3-1)L= 2atm.L = 202.7 J

a) Since V2>V1 and the work is positive , cycle is clockwise.

c) for a reversible engine

e = 1-Tc/Th

we have Tc= 273K  we need Th

Using the ideal gas law we find number of moles by using the known temp at point c PV=nRT

n = PV/RT = (1atm)(1L)/(.0821 atmL/molK)(273K) = .0446 mol

now we can find the temps at the other points

point a) T = PV/nR = (2 atm)(1L)/(.00366atmL/K) = 546 K

point b) T = PV/nR = (2atm)(3L)/(.00366 atmL/K) = 1639 K

point d) T = PV/nR = (1atm)(3L)/(.00366atmL/K) = 820 K

Th = 1639 K

plugging in

e = 1 - Tc/Th = 1 - 273/1639 = .833 e = 83.3%

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