Question

B.1 This question concerns the use of different working substances in an engine 2018 (a) Carbon monoxide (CO) and ethene (C2H4) are gases with the same molecular mass: how do you expect their heat capacities to compare, and why? A reversible heat engine involves one mole of diatomic ideal gas cycling around four states labelled a,b,c & d where a is the state of highest pressure. The cycle comprises two isotherms (a-b, c-d) and two isochores (b-c, d-a). [Note: 'isochore' means constant volume.] (b) Sketch the cycle on a PV indicator diagram, showing the direction around the cycle required to generate work. (c) Calculate the heat and work inputs and outputs in each part of the cycle, in terms of temperatures Ta, T. and volumes Va, Vc. (d) Identify the waste heat, and write an expression for the efficiency of the engine. (e) Use your expression for efficiency to predict whether using a triatomic ideal gas as the working fluid would improve the efficiency. (f) By comparing the ideal efficiency of this engine with the efficiency of a Carnot engine running between heat reservoirs at Tq and Tc, show that a working fluid with a negative heat capacity would violate the Second Law.

Answer 1

and CqHq ú diatomie while are gases Cz Hq is W Both co But co polyatomir specific heat a chatonne polyatonic There fore at constant volone for gas is Cu = 3 R gas is eva & cv for co is (SR) o for Cz He is ER P + c Process work process a b Isothrmal done on the system Wa-b = nRT l Ve

ginen n= I mole Warb = - Ría lng mork done by the systems is Warb = RTa en No Heat transfered to the gas is Q = nRla un = R ła no Pocens d e mork done by the systers is Watc = R Td us (Ve) is a ve Heat tranobud out of the systems is a = R Td ls (Vel is the d) waste of heat = R Ta lub) - R Ta in =R (Ta muo) - Ta la vida DQ = Q; - Q7

MO Effiuency of the endine is defined as r = Qi - Qt _R(Ta enco - Ta ln (Vd)) - Rłaln (o) But we have nak Talna) Tammel) va = vc - lud = Vb R Ta en (Vd) n = Ta-Td = 1- Td is the efficeny