A cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in Fig .

A to B : volume constant B to C : adiabatic C to D : volume constant D to A : adiabatic Vc=VD=2VA=2VB

(a) In which part of the cycle heat is supplied to the engine from outside?

(b) In which part of the cycle heat is being given to the surrounding by the engine?

(c) What is the work done by the engine in one cycle? Write your answer in term of PA, PB, VA

(d) What is the efficiency of the engine? [γ =5/3 for the gas], (Cv= 3/2R for one mole)

0 2 Views | Posted 4 months ago
Asked by Shiksha User

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    This is a long answer type question as classified in NCERT Exemplar

    (a) For the process AB

    dV=0 and dW=0

    dQ=dU+dW=dU

    dQ=dU= change in internal energy , so heat utilised is equal to change in internal energy.

    Since p= n R V T , in adiabatic temperature is directly proportional to pressure. So heat is supplied to the system in process AB.

    (b) For the process CD volume is constant but the pressure decreases, hence temperature also decreases . so heat is also given to the surroundings.

    (c) WAB= A B p d V = 0 , WCD= V c V d p d V = 0

    WBC= V B V c p d V = k V B V c d V V Y = k 1 - Y V 1 - Y  

    = 1 1 - Y [pV]= P c V c - P B V B 1 - Y

    WDA= P A V A - P D V D 1 - Y

    B and C lies on adiabatic curve BC

    PBVBY= PCVCY

    PC = PB( V B V C )Y = PB( 1 2 )Y= 2-YPB

    Total work done by the engine in one cycle ABCD

    ...more

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