Understanding P-V Diagrams: Work Done and Heat Input in a Closed Loop Process

[quietrain]

in a close loop P-V diagram,

dQ = dE + PdV right?

so if i want to get the net work down by the gas , i just need to find the Work done for each process right?

but my dE is always 0 since cyclic process,

so for constant volume,

WD = ∫ PdV = 0

for constant temperature,

WD = ∫ PdV = nrT∫ VdV = nrT ln V

for constant pressure,

WD = ∫ PdV = P(V₂-V₁)

so since dE is 0, heat input = work done by the gas right? since from First law,

heat in = change in internal energy + work done by the gas

so in calculating the work done by the gas, i am calculating the heat input right?

thanks!

 

[m.e.t.a.]

Your reasoning looks correct to me: for a cyclic process whereby a fixed quantity of ideal gas is returned to its initial (P, V) coordinates, the net change in internal energy is zero. $\Delta U = Q - W = 0$, so $Q = W$.

 

[Andrew Mason]

so since dE is 0, heat input = work done by the gas right? since from First law,

heat in = change in internal energy + work done by the gas

What do you mean by heat in? Qh or Qh-Qc?

$\Delta Q = W$. The net heat flow into the system = work done by the system. The net heat flow into the system is the heat flow from the hot reservoir (Qh) minus the heat flow to the cold reservoir (Qc).

So:

$$W = \Delta Q = Q_h-Q_c$$

AM

 

[quietrain]

ah i see thanks!

 

[PJC01]

I can confirm that your understanding of P-V diagrams and the relationship between work done and heat input is correct. In a closed loop process, the change in internal energy (dE) is indeed zero, so the heat input is equal to the work done by the gas. This is in line with the First Law of Thermodynamics, which states that the heat input is equal to the change in internal energy plus the work done by the system. Therefore, in calculating the work done by the gas in a closed loop P-V diagram, you are essentially calculating the heat input for the system. It is important to note that this relationship holds true only for closed loop processes, as in open systems, there may be other factors contributing to the change in internal energy. Overall, your understanding of P-V diagrams and the associated calculations is accurate and well-supported by scientific principles. Keep up the good work!