First Law of Thermodynamics: Energy Conservation Rule

The first law of thermodynamics is the law of conservation of energy applied to heat and mechanical work. It says the change in internal energy of a system equals heat added to the system minus work done by the system.

This law rules out perpetual motion machines that create energy from nothing. Every engine, living body, and power station must obey it, making it the starting point for all thermodynamics calculations.

Key Concepts

Internal energy U is a state function in joule. Heat Q is energy transfer due to temperature difference. Work W is energy transfer by expansion, compression, shaft rotation, or electrical means. Sign convention used here: Q positive when added to system, W positive when done by system, so delta U = Q - W. In chemistry convention work done on system is positive and formula becomes delta U = Q + W_on. A cyclic process returns to initial state, so delta U = 0 and Q_net = W_net.

Formulas

First law: delta U = Q - W_by. Expansion work: W_by = integral from V1 to V2 of P dV; for constant pressure W_by = P delta V, with P in pascal, volume in cubic metre, work in joule. Constant volume: W_by = 0 so Q_v = delta U. Constant pressure heat: Q_p = delta H, enthalpy change, useful for chemical reactions at atmospheric pressure.

Worked Example

A system receives 800 joule heat and does 300 joule work. Later it rejects 400 joule heat while 100 joule work is done on it. Find net delta U over both steps.

Step 1 first process: delta U1 = 800 - 300 = 500 joule. Step 2 second process: Q = -400 joule. Work done by system is -100 joule because work is done on it. delta U2 = -400 - (-100) = -300 joule. Step 3 total delta U = 500 - 300 = 200 joule. Internal energy ends 200 joule higher than start.

Common Misconceptions

• First law says heat is conserved: Wrong. Total energy is conserved; heat can convert to work and internal energy.
• If delta U is zero, no heat or work occurred: Wrong. In a cycle or isothermal ideal gas process, Q can equal W while delta U = 0.
• Sign of work is universal: Wrong. Physics and chemistry conventions differ; state your convention before calculating.

Real-World Applications

Steam turbines convert heat from fuel into shaft work while exhaust carries remaining energy. Diet and exercise follow first law for body energy stores. Refrigeration cycles use work input to move heat. Rocket engines, pressure cookers, and industrial furnaces are designed with energy balances from the first law.

The first law is energy bookkeeping: delta U = Q - W_by. It does not tell whether a process can happen, only that energy cannot appear or disappear, which is enough to solve many heat and engine problems.