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First Law of Thermodynamics (Energy Balance)
States that the change in internal energy of a closed system equals the heat added minus the work done by the system.
Interpretation
The first law of thermodynamics for a closed system: ΔU = Q − W. It states that the change in internal energy equals heat added minus work done by the system. This is the energy balance equation for thermal processes.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| delta_U | Change in internal energy | kJ |
| Q | Heat added to the system | kJ |
| W | Work done by the system | kJ |
What it means
The first law of thermodynamics is the application of energy conservation to thermodynamic systems. For a closed system (no mass transfer), the change in internal energy ΔU is equal to the net heat added to the system Q minus the work done by the system W: ΔU = Q − W. This equation is the cornerstone of thermal engineering. It is used to analyze heat engines, refrigerators, and compressors. The sign convention: positive Q is heat added to the system, positive W is work done by the system. The internal energy U is a state function, so its change depends only on the initial and final states. The first law can also be written in rate form for steady‑flow devices: Q̇ − Ẇ = ṁ Δh + ΔKE + ΔPE. This law enables calculation of energy efficiency and is essential for designing power plants, HVAC systems, and combustion processes. It is also the basis for the energy balance in chemical reactions.
Worked example
First Law (Energy Balance) – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Q | +500 kJ |
| W | +200 kJ |
| Parameter | Value |
|---|---|
| W_in | 100 kJ |
| Q_c | 200 kJ |
Common mistakes
- Sign convention (same as ID 15): Q positive when added, W positive when done by the system.
- Work “on” vs “by”: Be consistent with your textbook – some use ΔU = Q + W (work on).
- Closed system: This form does not include flow work; for open systems, use enthalpy.
- ΔU for ideal gas: Only temperature dependent; for real gases, volume/pressure also matter.
- Heat transfer vs. temperature: Q is energy, not temperature.
Applications
The first law of thermodynamics (energy balance) states that the change in internal energy of a system equals heat added minus work done. This principle is the bedrock of thermal engineering, used in the analysis of engines, turbines, compressors, and heat pumps. It enables engineers to perform energy audits, optimise fuel consumption, and design efficient thermal systems. In power plants, it is used to calculate the efficiency of steam and gas cycles. In refrigeration, it determines the coefficient of performance. The law also applies to chemical processes, where energy balances are essential for reactor design and safety. By applying the first law, engineers can identify energy losses and improve the overall performance of thermal systems.
- Power plant cycle analysis (Rankine, Brayton)
- HVAC system design and performance evaluation
- Chemical reactor energy balance
- Internal combustion engine heat loss analysis
- Energy storage system design
Frequently Asked Questions
The First Law is the principle of energy conservation. For a closed system, it states that the change in internal energy equals the heat added minus the work done by the system: ΔU = Q − W. It can also be written for a cycle (ΔU = 0) as Q_net = W_net.
- Q is positive when heat is added to the system.
- W is positive when work is done by the system (e.g., expansion).
- Using an inconsistent sign convention – mixing up whether W is done by or on the system.
- Ignoring the type of process – for adiabatic, Q=0; for isochoric, W=0.
- Confusing heat with work – both are energy transfers; the distinction depends on the boundary interaction.
- Not accounting for changes in kinetic or potential energy – the general form includes those if they are significant.
- Isochoric (constant volume): W = 0, so ΔU = Q.
- Isobaric (constant pressure): W = P·ΔV, so ΔU = Q − P·ΔV.
- Isothermal (constant temperature, ideal gas): ΔU = 0, so Q = W.
- Adiabatic (no heat exchange): Q = 0, so ΔU = −W.
Internal energy includes all microscopic energy (kinetic + potential) of the molecules. Enthalpy is defined as H = U + P·V. It is useful for processes at constant pressure, where the heat added equals the change in enthalpy (ΔH = Q_p). For flow processes, enthalpy is often more convenient than internal energy.
For a heat engine operating in a cycle, ΔU = 0, so Q_in − Q_out = W_net. The thermal efficiency is η = W_net / Q_in. For a refrigerator, the COP = Q_c / W (for cooling) or COP = Q_h / W (for heat pump). The First Law provides the energy balance that governs all these devices.
For a closed system (fixed mass), the equation is ΔU = Q − W. For an open system (control volume), the steady‑flow energy equation (SFEE) is:
Q − W = ṁ [ (h₂ − h₁) + ½(v₂²−v₁²) + g(z₂−z₁) ]. This includes flow work (Pv) which is why enthalpy h appears.
Yes, the First Law is always valid, regardless of reversibility. Energy conservation holds for all processes. However, the calculation of work and heat may require integration over the actual path, which is more complex for irreversible processes. The Second Law is needed to determine the direction and quality of energy transformations.
Heat is energy in transit due to a temperature difference; it is a process function (path‑dependent). Internal energy is a property (state function) that depends only on the current state of the system. A system does not 'contain' heat; it contains internal energy.
A throttling process is adiabatic (Q=0) and involves no work (W=0), so ΔU = 0. For an ideal gas, ΔT = 0 (isenthalpic). For real gases, the temperature may change (Joule‑Thomson effect). The First Law is used to set up the energy balance for expansion valves in refrigeration cycles.