Hypothetical cyclic process- does it violate the thermodynamic laws?

[trelek2]

Consider the following cyclic process:
Each cycle 800J of Energy is transferred from a reservoir at 800K and 600J of energy from a reservoir at 600K. 400J of heat is rejected to a reservoir at 400K and 1000J of work is done.

I think that the process doesn't violate the first or second laws of thermodynamics:
1st law: dU= dQ+dW
The internal energy of the system is constant: dU= 600+800-1000-400 = 0 so first law is not violated.
2nd law: Taking the Kelvin Planck statement: The engine not only extracts heat from a source and turns it into work but also has to pass some heat on to a colder reservoir, therefore I think that the second law is also not violated.
If I'm mistaken please correct me. If I'm not please reassure me that my logic is correct.

 

[jtbell]

Hint: consider the total change in entropy.

 

[trelek2]

We haven't really covered entropy in the lectures yet, so i don't think I'm ment to be using that. Nevertheless, I looked at it just now and it seems to me that the overall entropy of the system increases after each cycle, so the 2nd law is not violated, is that right?

 

[jtbell]

it seems to me that the overall entropy of the system increases after each cycle

How did you figure that?

 

[jtbell]

it seems to me that the overall entropy of the system increases after each cycle

How did you figure that?

 

[trelek2]

I found that the change in entropy is equal to amount of energy added or extracted at a given temperature. So we take out 1 twice and put back in once for sure. I'm not sure what to do with the work. I thought it would be increasing entropy of the surroundings by 1000J/700K which is over 1?