11.2.1 First law of thermodynamics

First Law of Thermodynamics Overview

The first law of thermodynamics is a principle of energy conservation in thermodynamic systems. It states that the energy transferred to a system through heating $( Q )$ is equal to the sum of the increase in internal energy $( \Delta U )$ and the work done by the system $( W )$. Mathematically, this is expressed as:

$$Q = \Delta U + W$$

Where:

• $Q$ is the energy added to the system via heating or cooling.
• $\Delta U$ is the change in internal energy of the system.
• $W$ is the work done by the system on its surroundings.

Understanding Internal Energy and Work

1. Internal Energy $( U )$:

• This is the total energy of a system, which includes both the kinetic energy of the particles (due to their motion) and their potential energy.
• An increase in internal energy $(\Delta U > 0)$ implies that the particles in the system are gaining energy, whereas a decrease $(\Delta U < 0 )$ implies they are losing energy.

2. Work Done ($$ W ):

• Work is done by the system when it expands against an external pressure, moving the boundary of the system (e.g., expanding gas).
• If $W$ is positive, the system is doing work on the surroundings (energy leaves the system).
• If $W$ is negative, work is being done on the system (energy is added to the system).

Open and Closed Systems

• Open System:
  • In an open system, gas can flow in and out of the system. Energy and matter can cross the boundary.
  • Example: An aerosol can, where gas can leave the container when sprayed.
• Closed System:
  • In a closed system, no gas can enter or leave, although energy may still transfer across the boundaries.
  • Example: A balloon with a fixed amount of air inside, but which may change shape or volume.

Practical Application: Human Metabolism

In biological systems, such as the human body, the first law of thermodynamics explains how internal energy changes due to heat and work. Here:

• $Q$ represents heat lost from the body (e.g., through skin to surroundings).
• $W$ represents work done by the body (e.g., muscle movements). For example, when exercising, the body transfers heat to the surroundings (negative $( Q )$ and does work (positive $( W )$, leading to a decrease in internal energy unless replenished by food energy.