Ever wondered why a hot cup of tea cools down while your hands feel warmer? That everyday magic is the first law of thermodynamics at work.
๐ก In Simple Words: Energy never disappears โ it just changes form. When you add heat to a system, some of that heat can turn into work, and whatever is left stays as internal energy.
What is the First Law of Thermodynamics?
The first law is a fancy way of saying energy is conserved. In physics, we call the total energy inside a system its internal energy (think of it as the energy stored in all the tiny motions of molecules). The law tells us how this internal energy changes when heat or work enters or leaves the system.
Understanding Energy, Heat, and Work
- Internal energy (U): the sum of kinetic (movement) and potential (position) energy of all particles in a substance.
- Heat (Q): energy transferred because of a temperature difference, like warm water heating a cold pot.
- Work (W): energy transferred when a force moves something, such as a piston being pushed.
Imagine a water tank with a pipe. Adding water is like adding heat โ it raises the level (energy). Opening a valve and letting water flow out is like doing work โ the water leaves, taking energy with it. Whatever water stays in the tank is the internal energy left behind.
Mathematical Form of the First Law
In symbols, the first law reads:
ฮU = Q โ W
Where:
- ฮU = change in internal energy (final minus initial).
- Q = heat added to the system (positive if heat enters, negative if it leaves).
- W = work done by the system on its surroundings (positive if the system does work, negative if work is done on the system).
Notice the minus sign before W. If the system does work, it loses some energy, so internal energy drops.
Worked Example: Gas in a Piston
Suppose 1 mole of an ideal gas is inside a piston. We heat the gas so that it receives Q = 500 J of energy. While heating, the gas expands and pushes the piston, doing W = 200 J of work on the surroundings. What is the change in internal energy?
Using ฮU = Q โ W:
ฮU = 500 J โ 200 J = 300 J
So the gasโs internal energy rises by 300 joules. If we had instead compressed the gas (work done on the system), W would be negative, making ฮU larger.
Key Points Summary
| Term | Meaning | Sign Convention |
|---|---|---|
| ฮU | Change in internal energy | Positive โ energy stored increases |
| Q | Heat transferred | Positive โ heat added to system |
| W | Work done by system | Positive โ system does work, loses energy |
- Energy cannot be created or destroyed, only transformed.
- Heat added to a system can become internal energy, work, or both.
- If no heat is added (Q = 0) and the system does work, its internal energy must drop (ฮU = โW).
- In an isolated system (no heat exchange, no work), ฮU = 0 โ the energy stays exactly the same.
Common Mistakes to Avoid
- Mixing up the sign of work. Remember: work done *by* the system is taken away from its energy.
- Thinking that heat and work are the same. They are both ways of moving energy, but they act through different mechanisms.
- Forgetting that internal energy is a state function โ it depends only on the initial and final states, not on how you got there.
๐ Likely Exam Questions
- State the first law of thermodynamics and explain each term.
Answer: The first law says the change in internal energy of a system equals the heat added to the system minus the work done by the system (ฮU = Q โ W). ฮU is the change in internal energy, Q is heat transferred (positive when added), and W is work done by the system (positive when the system expands). - A gas absorbs 800 J of heat and does 300 J of work on the piston. Find the change in its internal energy.
Answer: ฮU = Q โ W = 800 J โ 300 J = 500 J (internal energy increases). - Explain why the internal energy of an isolated system remains constant.
Answer: An isolated system exchanges neither heat nor work with its surroundings, so Q = 0 and W = 0. Hence ฮU = 0, meaning the total internal energy stays the same. - In a refrigeration cycle, the compressor does 1500 J of work on the gas while 1200 J of heat is removed from the interior of the fridge. What is the net change in internal energy of the gas?
Answer: Here work is done *on* the gas, so W is negative: W = โ1500 J. Heat removed from the interior means heat is added to the gas, Q = +1200 J. ฮU = Q โ W = 1200 J โ (โ1500 J) = 2700 J. - Differentiate between heat and work with an everyday example.
Answer: Heat is energy transferred because of a temperature difference, like a hot cup warming your hands. Work is energy transferred when a force moves something, like pushing a door open.