# Calculating the Absorbed Heat & the Change in Internal Energy of an undefined thermodynamic process In the given figure of a P-V diagram, the process from $$T_2$$ from $$T_3$$ (the hypotenuse part of the triangle) doesn't follow any of the 4 thermodynamic processes (i.e Isothermal, Isochoric, Isobaric, Adiabatic processes). The given system is of a gas (which is not necessarily an Ideal Gas) contained in a metal container having a frictionless piston.

The volume of the gas can be changed by moving the piston back and forth & the temperature of the gas can be changed by exchanging heat with its surroundings through the metal container. The question asks to find the absorbed heat & the change in internal energy of the system as the temperature of the system changes from $$T_2$$ to $$T_3$$ (the hypotenuse).

I couldn't find a satisfactory answer of what formulae should be used here even after searching in my textbooks. My friends said that we can use the "$$du=nC_v(T_3-T_2)$$" formula here for calculating the change in internal energy & the "$$dQ=nC_v(T_3-T_2)+ \frac{1}{2}(P_1+P_2)(V_2-V_1)$$" formula for calculating the absorbed heat in this process. But, why should we use these formulae here as this process is not a defined thermodynamic process & only a theoretical one? Is there any explanation as to why we should be using these formulae here? Can we even calculate the change in internal energy & the absorbed heat for this process (temperature going from $$T_2$$ to $$T_3$$)? If yes then kindly explain how.

I'm a high school junior & have not taken any Thermodynamics course, so a lot of things are yet unknown to me. It would be delightful for me if anyone would clear my doubts & provide a lucid explanation to my question.