How Do You Calculate Efficiency in a Carnot Cycle Involving Argon?

[stonecoldgen]

Homework Statement

its part VI) of a big problem, where:

0.12 moles of argon (40) undergoes the cycle abca described in the graph. Process ab lies on a 540k isotherm.

In the previious 5 sub problems, i figured that:

T_c=270k
Q_bc=670J (lost)
Q_ca=400J (added)
W_ab=370J
W_abca=100J


The PV diagram has points a,b and c where:

a=(1.5X10^-3, 3.6X10⁵)
b=(3X10^-3, 1.8X10⁵)
c=(1.5X10^-3, 1.8X10⁵)

Homework Equations

Q=mc$\Delta$T

$\Delta$U=Q+W

$\epsilon$=1-Q_out/Q_in=1-T_low/T_high

The Attempt at a Solution

So it's basically using Q_abca to find the efficiecy. The thing is that I am not sure what to use for the Qs.

 

[RTW69]

What is Q_s supposed to represent? I don't see it in your problem statement.

 

[stonecoldgen]

What is Q_s supposed to represent? I don't see it in your problem statement.

it's a plural for Q, I am not sure what to use for Q_in and Q_out

 

[RTW69]

Remember this is NOT a carnot cycle. η= 1- Q_out/Q_in There is also a Q_in between A and B. Do you know what it is? It is the Q_out/ the Total Q_in.

 

[asteriatic]

First, let's review the Carnot Cycle. This is a theoretical cycle that describes the most efficient way to convert heat into work. It consists of four processes: two isothermal processes and two adiabatic processes.

In your problem, you are given the temperature and moles of argon for one of the isothermal processes (ab), as well as the heat and work values for the entire cycle. To find the efficiency, we need to calculate the heat values for the other processes (bc and ca).

To do this, we can use the equation Q=mcΔT, where Q is the heat, m is the mass, and ΔT is the change in temperature. Since we are dealing with a gas, we can use the ideal gas law (PV=nRT) to find the change in temperature for each process.

For process bc, we know the initial and final volumes, so we can find the change in volume (ΔV) and use that to find the change in temperature. Similarly, for process ca, we know the initial and final pressures, so we can find the change in pressure (ΔP) and use that to find the change in temperature.

Once we have the heat values for all three processes (ab, bc, and ca), we can use the equation ΔU=Q+W to find the change in internal energy for the entire cycle. Since the Carnot Cycle is a closed cycle, the change in internal energy is equal to zero. We can then use the equation for efficiency, ε=1-Qout/Qin, to find the efficiency of the cycle.

I hope this helps with your homework problem. Remember to always check your units and make sure they are consistent throughout your calculations. Good luck!