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Thermodynamics 1st Law Equation

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Question on a system involving temperature, pressure and volume is attached.

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This set of thermodynamics problems is solved in a Word and PDF attachment.

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Hi there!

Here is my solution.

In the last part, the solution is very sensitive to the numerical value (there is an exponent there and we are dealing with quite large and small numbers).
#1) A system whose equation of state depends only on pressure P, volume V and temperature T is taken quasi-statically from state from state A to state B (in the figure shown above) along path ACB at the pressures indicated. In this process 50J of heat enter the system and 20J of work are done by the system.

How much heat enters the system along path ADB?

Energy is a variable of state. It means that the internal energy of the system depends only on the state and not on the thermodynamic path the system took to arrive at the state.

From state A to state C the system undergoes an isobaric process. This means that the work the system did during the process is:

From state C to state B the system undergoes an isochoric process (no change in volume), hence no work was performed during this step:

Therefore, the work done by the system going from state A to state B via the path ACB is:

Now, when the system goes from state A to state D, the process is isochoric (no change in volume), hence no work is performed by the system during this step:

When the system goes from state D top state B, the process is isobaric, but now the constant pressure is 5P1. Therefore, the work done by the system during this step is:

And the total work done along the path ADB is:

As we stated before, the change in the internal energy of the system is path-independent. No matter what path the system takes, the difference between the internal energy at state A to the internal energy at state B is the same.

Hence:

Now, we ...

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