What is the First Law of Thermodynamics?
The first law of thermodynamics is a restatement of conservation of energy for thermodynamic systems. It relates the change in internal energy to heat absorbed and work done by (or on) the system.
ΔU = Q − W: the change in internal energy equals heat absorbed minus work done by the system. Energy is conserved; none is created or destroyed.
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Step-by-step worked examples
A gas absorbs 3,000 J of heat and does 1,200 J of work on surroundings. What is ΔU?
ΔU = Q − W ΔU = 3000 − 1200 ΔU = +1800 J (internal energy increases)
A system releases 500 J of heat (Q = −500 J) and has 300 J of work done on it (W = −300 J). Find ΔU.
ΔU = Q − W ΔU = (−500) − (−300) ΔU = −500 + 300 = −200 J (internal energy decreases)
If ΔU = 400 J and the system does 600 J of work, how much heat is absorbed?
ΔU = Q − W 400 = Q − 600 Q = 400 + 600 = +1000 J
Flashcards
Quick quiz
Q1.A gas absorbs 4,500 J and does 2,000 J of work. What is ΔU?
Q2.What happens if Q = W?
Q3.A piston compresses a gas (work done on gas = 800 J). Heat released = 500 J. ΔU?
Q4.In an adiabatic process (Q = 0), what is ΔU?
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Common mistakes
Thinking ΔU = Q + W (adding work instead of subtracting). — Correct: ΔU = Q − W. Work done BY the system reduces internal energy.
Confusing sign convention: negative work means compression. — Correct: W > 0 = expansion (work done by system); W < 0 = compression (work done on system).
Assuming Q and W always have the same sign. — Correct: Q and W are independent. Heat in can occur during compression or expansion.
Forgetting that ΔU depends on state, not path. — Correct: ΔU is a state function; it depends only on initial and final states, not the process.
FAQ
Is the first law just 'conservation of energy'?
Yes, essentially. Energy input (heat) = internal energy change + work output.
What is the difference between heat and internal energy?
Heat is energy transfer due to temperature difference; internal energy is the total molecular energy in a system.
Can a system do work without absorbing heat?
Yes, if it has internal energy stored (e.g., compressed gas expanding adiabatically: Q = 0, but W > 0).
What is an adiabatic process?
A process where no heat is exchanged (Q = 0). All energy change is due to work: ΔU = −W.