Welcome to the World of Internal Energy!
Hello there! Today we are exploring Internal Energy, a core part of Thermodynamic Systems. Have you ever wondered why a bicycle pump gets hot when you use it, or why steam can move a massive train? It all comes down to the energy hidden inside the particles of a substance. By the end of these notes, you’ll understand how heat, work, and internal energy play together to power our world.
Don't worry if this seems a bit abstract at first—we’ll break it down piece by piece with plenty of analogies!
1. What exactly is Internal Energy?
In Physics, we look at the "microscopic" level—the world of tiny atoms and molecules. The internal energy (\(U\)) of a system is the sum of a random distribution of microscopic kinetic and potential energies associated with the molecules of the system.
Breaking it down:
- Microscopic Kinetic Energy (KE): This comes from the random movement of particles (vibrating, rotating, or flying around).
- Microscopic Potential Energy (PE): This comes from the intermolecular forces between the particles. Think of these like tiny invisible springs connecting the molecules.
- Random Distribution: This is key! We aren't talking about the whole box of gas moving (that's macroscopic KE); we are talking about the chaotic, messy movement of the individual particles inside.
Analogy: Imagine a busy dance floor. The Kinetic Energy is how fast the dancers are moving and spinning. The Potential Energy is the "social tension" or distance between them—how much they are pulling away or pushing toward each other.
Key Takeaway: \( U = \text{Sum of microscopic KE} + \text{Sum of microscopic PE} \)
2. Temperature and Kinetic Energy
There is a very special relationship between how hot something is and how fast its particles move. The thermodynamic temperature of a system is directly proportional to the mean (average) microscopic kinetic energy of its particles.
Did you know? At a temperature of Absolute Zero (0 K), the particles have their minimum possible kinetic energy. They don't necessarily stop completely (due to quantum mechanics), but they are as still as they can possibly be!
Quick Review: If you double the Kelvin temperature of an ideal gas, you are essentially doubling the average speed-squared (and thus the KE) of the particles.
3. Thermal Equilibrium and the Zeroth Law
Before we can talk about energy changing, we need to know when it stops moving. When two objects are in thermal contact, energy (heat) always flows from the object at a higher temperature to the one at a lower temperature.
Eventually, they reach the same temperature. At this point, there is no net energy transfer between them. We call this thermal equilibrium.
The Zeroth Law of Thermodynamics
This law sounds a bit like a logic puzzle: If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then A and B must be in thermal equilibrium with each other.
Why it matters: This law allows us to define temperature and use thermometers! If the thermometer (C) reads 37°C for you (A) and 37°C for a cup of water (B), we know you and the water are at the same temperature.
4. Work Done by a Gas
Gas can do work! Think of a piston in a car engine. When the gas expands, it pushes the piston up.
The work done by a gas when it expands against a constant external pressure (\(p\)) is given by:
\( W = p\Delta V \)
Where:
\(p\) = pressure (in Pascals, Pa)
\(\Delta V\) = change in volume (in \(m^3\))
Important: The Sign Convention
This is where many students get tripped up. In the H2 syllabus, we usually focus on the work done ON the gas (\(W\)).
- Compression: You push the piston down (Volume decreases). You are doing work on the gas. \(W\) is positive (+).
- Expansion: The gas pushes the piston up (Volume increases). The gas is doing work on the surroundings, which means work done on the gas is negative (-).
Key Takeaway: If the gas gets squashed, it gains energy (\(+W\)). If the gas expands, it loses energy (\(-W\)).
5. The First Law of Thermodynamics
This is the "Big Boss" equation of this chapter. It is simply the Law of Conservation of Energy applied to thermal systems.
The law states: The increase in internal energy (\(\Delta U\)) of a system is equal to the sum of the heat energy transferred to the system (\(Q\)) and the work done ON the system (\(W\)).
Equation: \( \Delta U = Q + W \)
How to use the signs (The "Bank Account" Analogy):
Think of Internal Energy (\(U\)) as your bank balance.
- \(Q\) is like a deposit/withdrawal of heat:
If heat is supplied to the system, \(Q\) is positive (+).
If the system loses heat to the surroundings, \(Q\) is negative (-). - \(W\) is like work done on the account:
If you do work on the gas (compression), \(W\) is positive (+).
If the gas does work (expansion), \(W\) is negative (-).
Common Mistake: Always check if the question says "work done by the gas" or "work done on the gas." If it says work done by the gas is 50J, then \(W\) in our formula must be -50J!
6. Specific Heat Capacity and Latent Heat
Sometimes when you add heat (\(Q\)), the temperature rises. Other times, the substance stays at the same temperature but changes state (like ice melting).
Specific Heat Capacity (\(c\))
This is the energy required to raise the temperature of 1 kg of a substance by 1 K (or 1°C).
\( Q = mc\Delta \theta \)
Specific Latent Heat (\(L\))
This is the energy required to change the state of 1 kg of a substance without a change in temperature.
\( Q = mL \)
- Latent Heat of Fusion (\(L_f\)): For melting/freezing.
- Latent Heat of Vaporisation (\(L_v\)): For boiling/condensing.
Connection to Internal Energy:
- During temperature change, the added heat increases the microscopic Kinetic Energy of the particles.
- During state change (melting/boiling), the added heat increases the microscopic Potential Energy as particles break free from their bonds. The temperature stays constant because the average KE isn't increasing!
Quick Review Box
Internal Energy (\(U\)): Sum of random microscopic KE + PE.
Temperature (\(T\)): Proportional to average microscopic KE.
First Law: \( \Delta U = Q + W \) (Energy is conserved!).
Work: \( W = p\Delta V \) (Positive if volume decreases).
State Change: Temperature is constant; only microscopic PE changes.
You've got this! Thermodynamics is just a big game of keeping track of where the energy goes. Practice a few First Law calculation questions, and you'll be a pro in no time!