First Law

The first law of thermodynamics is conservation of energy wearing a lab coat. Energy cannot be created or destroyed — it can only be transferred as heat or used to do work. The first law tells you exactly how to keep the energy books balanced for any thermodynamic process.

If you’ve internalized the conservation-of-energy idea from work-and-energy in §2.6, you’re already 80% of the way there. The first law just adds a little bookkeeping: which kinds of energy flow count as heat, which count as work, and what happens when both are happening at once.

The Bank Account Analogy

Think of a gas as a bank account. The “balance” is the internal energy (U) of the gas. There are two ways to change the balance:

• Deposits - heat flowing into the system (Q > 0) or work done on the system
• Withdrawals - heat flowing out (Q < 0) or work done by the system

The Equation

Sign Conventions

This is where most students get tripped up. Using the convention ΔU = Q - W:

Internal Energy

Internal energy (U) is the total kinetic and potential energy of all the molecules in the system. For an ideal gas, it depends only on temperature:

• Monatomic ideal gas: U = ($\frac{3}{2}$)nRT
• Diatomic ideal gas: U = ($\frac{5}{2}$)nRT

The key insight: for an ideal gas, if ΔT = 0, then ΔU = 0 no matter what else happens. This is enormously useful for isothermal processes (Section 3.8).

State Functions vs. Path Functions

This distinction is tested repeatedly on the MCAT.

State functions depend only on the current state of the system (like your bank balance - it doesn’t matter how you earned the money). Internal energy (U), temperature (T), pressure (P), and volume (V) are all state functions.

Path functions depend on how you got from one state to another. Heat (Q) and work (W) are path functions. The same starting and ending states can involve very different amounts of heat and work depending on the process taken.

Applying the First Law

Example 1: A gas absorbs 500 J of heat and does 200 J of work expanding against a piston.

ΔU = Q - W = 500 - 200 = 300 J. The internal energy (and temperature) increases.

Example 2: A gas is compressed (300 J of work done on it) while 100 J of heat escapes.

Q = -100 J (heat out), W = -300 J (work done on the system, not by it)

ΔU = Q - W = (-100) - (-300) = -100 + 300 = 200 J. Internal energy increases despite the heat loss, because the compression added even more energy.

Connection to Gen Chem

The first law is the physics version of energy conservation. In General Chemistry - Thermochemistry, you will see the same ideas expressed through enthalpy (H = U + PV), Hess’s law, and standard enthalpies of formation. The physics side focuses on PV work and gas behavior; the chemistry side focuses on reaction energetics. The MCAT tests both perspectives.