first law thermodynamics
Overview
# First Law of Thermodynamics - A-Level Physics Summary ## Key Learning Outcomes The First Law of Thermodynamics establishes the principle of energy conservation in thermodynamic systems, stating that ΔU = Q - W, where the change in internal energy (ΔU) equals heat supplied to the system (Q) minus work done by the system (W). Students must understand sign conventions, apply this law to various thermodynamic processes (isothermal, adiabatic, isochoric, and isobaric), and interpret energy transfers on p-V diagrams. This topic is fundamental for A-Level examinations, regularly appearing in both structured questions requiring numerical calculations and extended-response questions demanding conceptual understanding of energy transformations in gases and heat engines.
Core Concepts & Theory
The First Law of Thermodynamics is a statement of energy conservation applied to thermodynamic systems. It states: The increase in internal energy of a system equals the heat supplied to the system plus the work done on the system.
Mathematical Expression: $$\Delta U = Q + W$$
Where:
- ΔU = change in internal energy (J) — the total kinetic and potential energy of molecules
- Q = heat energy transferred to the system (J) — positive when heat enters the system
- W = work done on the system (J) — positive when work is done on the system (compression)
Cambridge Definition: Internal energy is the sum of the random distribution of kinetic and potential energies of molecules in a system.
Sign Conventions (Critical for A-Level):
- Q is positive when heat flows into the system
- Q is negative when heat flows out of the system
- W is positive when work is done on the system (compression)
- W is negative when work is done by the system (expansion)
Work Done by/on a Gas: $$W = -p\Delta V$$
The negative sign indicates work done by the gas during expansion. When a gas expands (ΔV > 0), it does work on surroundings, so W is negative.
Mnemonic: "HEAT IN + WORK ON = INTERNAL UP" — positive contributions increase internal energy.
Key Applications:
- Isothermal processes (ΔU = 0, so Q = -W)
- Adiabatic processes (Q = 0, so ΔU = W)
- Isochoric processes (W = 0, so ΔU = Q)
Detailed Explanation with Real-World Examples
Real-World Applications:
1. Car Engines (Otto Cycle): During the compression stroke, work is done on the air-fuel mixture (W positive), increasing internal energy and temperature. During the power stroke, combustion adds heat (Q positive), further increasing ΔU. The gas then expands, doing work on the piston (W negative), converting internal energy to mechanical work.
2. Refrigerators: A refrigerator removes heat from its interior (Q negative for the interior). A compressor does work on the refrigerant (W positive), increasing its internal energy. The hot refrigerant then releases heat to the surroundings through condenser coils, completing the cycle.
3. Bicycle Pump: When you rapidly compress air in a pump, you do work on the gas (W positive). If compression is quick (approximately adiabatic, Q ≈ 0), then ΔU = W, so internal energy increases significantly. The pump feels warm because molecular kinetic energy (temperature) increases.
Helpful Analogies:
Bank Account Analogy: Think of internal energy as your bank balance. Heat (Q) is like deposits/withdrawals, and work (W) is like income/expenses. Your balance change (ΔU) equals money in (Q + W). Just as deposits increase your balance, heat into the system increases internal energy.
Energy Pathway Visualization: Imagine internal energy as a reservoir. Heat and work are two different pathways for energy to enter or leave. The First Law says: whatever goes in minus whatever goes out equals what stays.
Cambridge Context: Exam questions often describe practical scenarios (engines, atmospheric processes) requiring you to identify Q, W, and ΔU with correct signs.
Worked Examples & Step-by-Step Solutions
**Example 1: Gas Expansion** *A gas expands at constant pressure of 2.0 × 10⁵ Pa from volume 0.30 m³ to 0.50 m³. During expansion, 8.0 × 10⁴ J of heat enters the gas. Calculate the change in internal energy.* **Solution:** **Step 1:** Calculate work done by the gas: $$W_{by} = p\Delta V = 2.0 \ti...
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Key Concepts
- First Law of Thermodynamics: The principle of energy conservation applied to thermodynamic systems, stating that energy cannot be created or destroyed.
- Internal Energy (U): The total energy contained within a thermodynamic system, comprising the kinetic and potential energies of its constituent particles.
- Heat (Q): Energy transferred between a system and its surroundings due to a temperature difference.
- Work (W): Energy transferred between a system and its surroundings due to a force acting over a distance, often associated with changes in volume.
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Exam Tips
- →Always pay close attention to the **sign conventions** for Q and W. A common mistake is to get these signs wrong, leading to incorrect calculations.
- →Remember that **internal energy (U) is a state function**, meaning ΔU only depends on the initial and final states, not the path. Q and W are path-dependent.
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