Can a carnot engine work if its sink and source are interchanged ? Class 11 thermodynamics
Answers
Answer:
A Carnot engine is named after Carnot scientist.
It is a reversible heat engine operating between two temperatures.
It has a maximum efficiency which no other engine can have.
Conditions of a reversible engine
It should be quasi static which means the change happens gradually that we do not notice the change happening
It should be non dissipative – No loss due to friction or any other thing
Theory
Consider a Heat engine, hot reservoir at a temperature T1 (Source of heat) and a cold reservoir at a temperature T2 (Sink of heat). The heat engine consists of the perfect gas which acts as a working substance.
The carnot cycle consists of 4 steps –
Heat is absorbed from the hot reservoir without change in temperature - Isothermal expansion
Increase of temperature in the heat engine from T1 to T2 so as to perform step 3 with same temperature gradient; There should not be any heat release during this process – Adiabatic expansion
Heat engine releases heat Q2 to sink at temperature T2 without change in temperature – Isothermal compression
Resetting the temperature back so as the repeat the cycle again. Hence, without heat release temperature changes from T2 to T1 – Adiabatic compression
Work done
Isothermal expansion of gas – Q1 is the amount of heat absorbed in this process and gas changes its volume and pressure from A(V1 , P1) to B(V2 , P2). Since it is expansion volume increases from V1 to V2 . There is no change in temperature and it remains at T1 This is represented in the graph as AB where we can notice increase in volume and decrease in pressure. So for simplicity, we can say Isothermal expansion process as change from A (V1 , P1,T1) to B (V2 , P2,T1)
Work done by the gas W1 = Q1 = = RT1 loge(V2/V1) = Area ABMKA
The above derivation is based on the standard gas equation PV = RT. It is actually work done in an isothermal expansion and if we do that here it will take us off the topic.
Adiabatic expansion of gas – Temperature changes from T1 to T2 The gas changes its volume and pressure from B(V2 , P2) to C(V3 , P3). Since it is expansion, volume increases from V2 to V3 and pressure decreases. This is represented in the graph as BC where we can notice increase in volume and decrease in pressure. So for simplicity, we can say adiabatic expansion process as change from B (V2 , P2,T1) to C (V3, P3,T2)
Work done by the gas W2 = = R (T2 – T1)/ (1 - ϒ) = Area BCNMB
The ϒ here is equal to Cp / Cv which is ratio of specific heat of gas at constant pressure to specific heat of gas at constant volume; Also, the above derivation which is actually work done in an adiabatic expansion, will take us off the topic here.
Isothermal compression on the gas – Q2 is the amount of heat released in this process and since it is a compression process, volume decreases here. There is no change in temperature. This is represented in the graph as CD where we can notice decrease in volume and increase in pressure. So for simplicity, we can say Isothermal compression process as change from C (V3 , P3,T2) to D (V4 , P4, T2)
Work done on the gas W3 = Q2 = = - RT2 loge(V4/V3) = RT2 loge(V3/V4) = - Area CDLNC
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Answer:
Yes, It can