Which equation best expresses the first law of thermodynamics, assuming [tex]Q[/tex] is heat, [tex]U[/tex] is internal energy, and [tex]W[/tex] is work?
A. [tex]\Delta W=\Delta Q+\Delta U[/tex]
B. [tex]\Delta W=\Delta U-\Delta Q[/tex]
C. [tex]\Delta Q=\Delta U+W[/tex]
D. [tex]\Delta U=Q-W[/tex]
Answer (1)
The first law of thermodynamics relates changes in internal energy to heat and work.
Express the first law mathematically as Δ U = Q − W .
Compare the equation to the given options.
The correct equation is Δ U = Q − W .
Explanation
Understanding the First Law of Thermodynamics The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In mathematical terms, this can be expressed as:
Expressing the Law Mathematically Δ U = Q − W
Identifying the Correct Option Comparing this equation with the given options, we find that option D matches our derived equation.
Conclusion Therefore, the equation that best expresses the first law of thermodynamics is:
Final Answer Δ U = Q − W
Examples
The first law of thermodynamics is crucial in understanding energy transformations in various real-world scenarios. For example, consider a car engine. When fuel is burned (heat added, Q ), some of that energy increases the internal energy of the system (raising the temperature of the engine, Δ U ), while the rest does work by pushing the pistons and ultimately moving the car ( W ). The first law helps engineers design more efficient engines by quantifying these energy transfers and minimizing wasted energy.
