1. Apply the first law of thermodynamics to a heat engine

For a cyclic heat engine, $\Delta U = 0$ so by the first law, $Q_{\text{net}} = W$ where $Q_{\text{net}}$ is the net heat absorbed by the engine and $W$ is the work done by the engine.

2. Interpret the given data

The engine absorbs heat $Q_1$ at temperature $T_1$ and heat $Q_2$ at temperature $T_2$. So total heat absorbed is $Q_{\text{net}} = Q_1 + Q_2$

Given work done is $W = J(Q_1 + Q_2)$ Here $J$ is the mechanical equivalent of heat, used when converting heat units to work units.

3. Check consistency with the first law

If $Q_1 + Q_2$ is heat quantity and work is expressed in mechanical units, then $W = J(Q_1 + Q_2)$ is exactly the proper conversion form of the first law.

Thus, this does not violate the first law.

4. Evaluate options

• A: violates 1st law of thermodynamics — False
• B: violates 1st law of thermodynamics if $Q_1$ is positive — False
• C: violates 1st law of thermodynamics if $Q_1$ is negative — False
• D: does not violate 1st law of thermodynamics — True

5. Conclusion

The given data is consistent with the first law of thermodynamics.

Therefore, the correct option is: $\boxed{D}$

6. Comparison with stored answer

Stored correct answer is A, but the thermodynamic relation given is consistent with the first law, so I disagree with the stored answer.