Work extracted from a general cycle

[Pushoam]

Homework Statement

In each cycle, the heat given to the system from the reservoir is dQ$_i$. So, why is the total work given by summing $dQ_i$ over the cycle,why not only $dQ_i$?

Homework Equations

The Attempt at a Solution

 

[DrClaude]

In each cycle, the heat given to the system from the reservoir is dQ$_i$.

That's not what the text says: "Heat dQ_i enters at a particular part of the cycle." In the picture, it is represented by the solid arrow.

 

[DrClaude]

By the way these kind of questions, which are not textbook problems but are related to an understanding of what is in the textbook, are not well suited to the homework forum. Instead, post in General Physics.

 

[Pushoam]

That's not what the text says: "Heat dQi enters at a particular part of the cycle." In the picture, it is represented by the solid arrow.

So, heat enters only through that particular part of the process. For the rest of the part of the process, the heat doesn't enter the system from the reservoir. This is what I understood.
Does the book mean that the infinitesimal heat enters at all infinitesimal parts of the cycle?

 

[Pushoam]

By the say these kind of questions, which are not textbook problems but are related to an understanding of what is in the textbook, are not well suited to the homework forum. Instead, post in General Physics.

I will take care of this from next time.

 

[DrClaude]

So, heat enters only through that particular part of the process. For the rest of the part of the process, the heat doesn't enter the system from the reservoir. This is what I understood.

That's not correct. Heat $dQ_i$ enters only during part $i$ of the cycle, but heat can enter at other places in the cycle, hence the sum over all the $dQ_i$ during the cycle.

 

[Pushoam]

That's not correct. Heat dQidQidQ_i enters only during part iii of the cycle, but heat can enter at other places in the cycle, hence the sum over all the dQidQidQ_i during the cycle.

O.K.
Now, I understood.
If the whole cycle is divided into n parts, then at ith part, the heat dQ_i enters the system.