Calculating Q Transferred in PV Graphs | Thermodynamics

[Dooh]

How do i calculate Q transferred in a PV graph (Pressure / Volume)? More specifcally, when it is a slope. All that was given is pressure and volume from the graph.

Also, in an isochoric process, how would one go about finding Q? I spent so much time on thermodynamics yet i still don't know how to find it.

 

[mezarashi]

Generally, there is no direct way to do so. You have to consider that

$$U = Q - W$$

The internal energy is dependant on temperature. Work is always a function of pressure and change in volume. There are interesting relationships for example if the process is adiabatic, so it depends on the situation. A combination of the ideal gas equation, adiabatic equation or use of saturation/compressed water/refrigerant tables may be needed depending on your problem.

 

[quicknote]

To calculate Q transferred in a PV graph, you can use the formula Q = ΔU + W, where Q is the heat transferred, ΔU is the change in internal energy, and W is the work done. In a PV graph, the work done is represented by the area under the curve. So, to find Q, you would need to calculate the change in internal energy and the work done and then add them together.

To find the change in internal energy, you can use the equation ΔU = nCvΔT, where n is the number of moles of gas, Cv is the molar specific heat capacity at constant volume, and ΔT is the change in temperature. You can use the pressure and volume values from the graph to determine the change in temperature using the ideal gas law, PV = nRT.

In an isochoric process, the volume remains constant, so the work done is zero. Therefore, to find Q, you can simply use the formula Q = ΔU. Again, you would need to determine the change in internal energy using the equation mentioned above.

I understand that thermodynamics can be complex and it takes time to fully understand all the concepts. I would suggest seeking help from a tutor or your professor if you are struggling with finding Q in different processes. With practice and understanding of the concepts, you will be able to solve these problems more easily.