Question
Describe the working of Carnot engine. Obtain an expression for its efficiency.
✓
Answer
Carnot used a set of four devices—a source at a high temperature (say T1), a sink at a low temperature (say T2), a non-conducting base and a cylinder with a working substance, frictionless piston made of conducting base and non-conducting walls and piston.
He carried the system through a step of four processes to complete a cycle as shown here.
Process I-HW is an isothermal expansion. Q1 energy flows in and temperature is maintained at T1 by placing the cylinder over the source.
Process II-WN is an adiabatic processes at a temperature flow from T1 to T2 conducted with cylinder over (NCB = Non conducting base).
Process III-NF is an isothermal process at T2 which gives out an energy Q2 with cylinder over sink
Process IV-FH is an adiabatic process which changes the temperature from T2 to T1 conducted with the cylinder placed over (NCB = Non conducting base).
In the process, a net work equalling the area HWNFH is done with the net heat intake,
Q1 - Q2 So, Efficiency $=\frac{\text{Work done}}{\text{heat supplied}}$
$=\frac{\text{Q}_1-\text{Q}_2}{\text{Q}_1}=1-\frac{\text{Q}_2}{\text{Q}_1}=1-\frac{\text{T}_2}{\text{T}_1}$
He carried the system through a step of four processes to complete a cycle as shown here.
Process I-HW is an isothermal expansion. Q1 energy flows in and temperature is maintained at T1 by placing the cylinder over the source.
Process II-WN is an adiabatic processes at a temperature flow from T1 to T2 conducted with cylinder over (NCB = Non conducting base).
Process III-NF is an isothermal process at T2 which gives out an energy Q2 with cylinder over sink
Process IV-FH is an adiabatic process which changes the temperature from T2 to T1 conducted with the cylinder placed over (NCB = Non conducting base).
In the process, a net work equalling the area HWNFH is done with the net heat intake,
Q1 - Q2 So, Efficiency $=\frac{\text{Work done}}{\text{heat supplied}}$
$=\frac{\text{Q}_1-\text{Q}_2}{\text{Q}_1}=1-\frac{\text{Q}_2}{\text{Q}_1}=1-\frac{\text{T}_2}{\text{T}_1}$
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