Thermodynamics - Work/Heat question

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The discussion centers on a thermodynamics problem involving a gas system transitioning between states with specific heat and work values. The user questions their interpretation of the work done during a process where 40 J of heat is expelled, wondering if their application of the equation DQ = -DW is valid for a non-closed path. Participants suggest considering the change in internal energy and relevant equations that connect internal energy, heat, and work. The user seeks clarification on whether the work is done on or by the system in this context. Understanding the implications of the first law of thermodynamics is crucial for solving the problem accurately.
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Hi guys,
So I have a question in a piece of coursework which I seem to have done too simply, its worth 7 marks and I am thinking I've missed something somewhere so was hoping to run it by someone else.

1. Homework Statement

A system consists of gas contained in a cylinder fitted with a frictionless piston and
is taken from the state b to the state a along the path b  d  a shown in the
figure below. During this process 50 J of heat flow from the system and 25 J of
work is done on the system.
upload_2015-10-25_14-55-10.png

How much work is done when the system is taken along the path b  c  a if
40 J of heat are expelled by the system? Is it done on or by the system?

Homework Equations


DQ=-DW

The Attempt at a Solution


I have simply said that since 40J of heat flows from the system, 40J of work is done on the system. Due to the above equation. My only thought is that perhaps this equation doesn't hold for B to C to A since the path is not closed? If anyone can point me in the right direction I would be very grateful :)
Thanks
 
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Think about the change in internal energy of the system. What equations do you know that relate internal energy, heat and work?
 
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