For each of the cases below, determine if the heat engine satisfies the first law (energy equation) and if it violates the second law.
1. ˙qh=6 kw,˙ql=4 kw,˙w=2 kw
2. ˙qh=6 kw,˙ql=0 kw,˙w=6 kw
3. ˙qh=6 kw,˙ql=2 kw,˙w=5 kw
4. ˙qh=6 kw,˙ql=6 kw,˙w=0 kw

From first law of thermodynamics(energy conservation)

Qa= Qr+W

Qa=Heat added to the engine

Qr=heat rejected from the engine

W=work output from the engine

Second law:

It is impossible to construct a heat engine that will deliver the work with out rejecting heat.

In other word ,if engine take heat then it will reject some amount heat and will deliver some amount of work.

1.

QH=6 kW,

QL=4 kW,

W=2 kW

6 KW= 4 + 2  KW

It satisfy the first law.

Here heat is also rejected from the engine that is why it satisfy second law.

2.

QH=6 kW, QL=0 kW, W=6 kW

This satisfy first law but does not satisfy second law because heat rejection is zero.

3.

QH=6 kW   ,   QL=2 kW,      W=5 kW

This does not satisfy first as well as second law.Because summation of heat rejection and work can not be greater than heat addition or we can say that energy is not conserve.

4.

QH=6 kW,   QL=6 kW,   W=0 kW

This satisfy first law only and does not satisfy second law.