Thermodynamics ki foundation laws of energy par based hai, aur unme se sabse pehla aur fundamental hai First Law of Thermodynamics. Ye law energy conservation ka principle define karta hai aur heat, work, aur internal energy ke relationship ko describe karta hai.
1. Introduction
Thermodynamics ek branch hai jo energy ke transfer aur transformation ko study karti hai. Pehla law, ya Law of Energy Conservation, kehta hai:
Energy na to create ki ja sakti hai na destroy, sirf ek form se doosri form me convert ki ja sakti hai.
Is law ke through hum heat engines, refrigerators, chemical reactions, aur biological systems ke energy balance ko analyze karte hain.
2. Statement of First Law
2.1 Classical Statement
First Law of Thermodynamics kehta hai:
The increase in the internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings.
Mathematically: ΔU=Q−W\Delta U = Q – WΔU=Q−W
Where:
- ΔU\Delta UΔU = change in internal energy of the system (J)
- QQQ = heat added to the system (J)
- WWW = work done by the system (J)
Sign Convention:
- Q>0Q > 0Q>0 → Heat added to system
- Q<0Q < 0Q<0 → Heat removed from system
- W>0W > 0W>0 → Work done by system
- W<0W < 0W<0 → Work done on system
2.2 Alternate Statement
Energy can be transformed from one form to another, but the total energy of an isolated system remains constant.
- This is the law of energy conservation applied to thermodynamic systems.
3. Concept of Internal Energy
Internal energy (U):
- Total energy possessed by a system due to microscopic motion and interactions of its particles.
- Components:
- Kinetic energy of molecules (translational, rotational, vibrational)
- Potential energy due to intermolecular forces
Key Points:
- Internal energy is a state function → depends only on current state, not the path.
- For ideal gases, internal energy depends only on temperature.
Mathematical expression for ideal gas: U=f2nRTU = \frac{f}{2} n R TU=2fnRT
Where:
- fff = degrees of freedom of gas molecules
- nnn = number of moles
- RRR = universal gas constant
- TTT = temperature in Kelvin
4. Work and Heat in Thermodynamics
4.1 Work (W)
- Work is energy transfer due to macroscopic forces.
- For a gas expanding/compressing in piston:
W=∫PdVW = \int P dVW=∫PdV
Where PPP = pressure, dVdVdV = change in volume
- Work done by system → energy leaves system
- Work done on system → energy enters system
4.2 Heat (Q)
- Heat is energy transfer due to temperature difference.
- Positive when absorbed by system, negative when released.
5. Mathematical Formulation
For infinitesimal changes: dU=δQ−δWdU = \delta Q – \delta WdU=δQ−δW
- dUdUdU = exact differential (state function)
- δQ,δW\delta Q, \delta WδQ,δW = inexact differentials (path functions)
6. Application to Thermodynamic Processes
6.1 Isothermal Process (ΔT = 0)
- For ideal gas, ΔU = 0
Q=WQ = WQ=W
- Heat added to system is completely converted into work.
Example: Slow expansion of ideal gas at constant temperature in piston.
6.2 Adiabatic Process (Q = 0)
- No heat exchange with surroundings
ΔU=−W\Delta U = -WΔU=−W
- Work done by system decreases internal energy.
Equation for ideal gas: PVγ=constantwhere γ=CpCvP V^\gamma = \text{constant} \quad \text{where } \gamma = \frac{C_p}{C_v}PVγ=constantwhere γ=CvCp
6.3 Isochoric Process (V = constant)
- Volume constant → W = 0
ΔU=Q\Delta U = QΔU=Q
- All heat added increases internal energy.
6.4 Isobaric Process (P = constant)
- Constant pressure → W = PΔV
ΔU=Q−PΔV\Delta U = Q – P\Delta VΔU=Q−PΔV
7. Graphical Representation
- P-V Diagram: Work done = area under curve
- T-S Diagram: Heat transfer = area under curve
P
|
| *
| / \
| / \
| / *
|____/________ V
8. First Law for Cyclic Processes
- In a cyclic process, system returns to original state → ΔU = 0
- Therefore:
Q=WQ = WQ=W
- Heat absorbed = work done → basis for heat engines
9. First Law for Open Systems
- Control volume analysis: mass enters and leaves
- Energy balance equation:
ΔU+ΔKE+ΔPE=Q−W+∑(minhin)−∑(mouthout)\Delta U + \Delta KE + \Delta PE = Q – W + \sum (m_{in} h_{in}) – \sum (m_{out} h_{out})ΔU+ΔKE+ΔPE=Q−W+∑(minhin)−∑(mouthout)
- hhh = specific enthalpy, KE = kinetic energy, PE = potential energy
10. Examples and Calculations
Example 1: Heating Gas in Piston
- 1 kg ideal gas, Cv = 718 J/kg·K, ΔT = 10 K, piston does 2000 J work.
ΔU=mCvΔT=1×718×10=7180J\Delta U = m C_v \Delta T = 1 \times 718 \times 10 = 7180 JΔU=mCvΔT=1×718×10=7180J Q=ΔU+W=7180+2000=9180JQ = \Delta U + W = 7180 + 2000 = 9180 JQ=ΔU+W=7180+2000=9180J
Example 2: Adiabatic Expansion
- Gas does 5000 J work on surroundings, Q = 0
ΔU=−W=−5000J\Delta U = – W = -5000 JΔU=−W=−5000J
11. Applications of First Law
- Heat Engines
- Convert heat into work
- Efficiency depends on Q and W
- Refrigerators and Heat Pumps
- Work input moves heat from cold to hot region
- Chemical Reactions
- Determine heat released/absorbed
- Biological Systems
- Energy metabolism in human body
- Engineering Systems
- Boilers, turbines, internal combustion engines
12. Limitations
- First law does not predict direction of process
- Does not define efficiency limit → requires Second Law
13. Historical Context
- First law established in mid-19th century
- James Joule demonstrated mechanical work converts to heat
- Foundation for energy conservation in thermodynamic systems
14. Summary Table
| Process | Heat (Q) | Work (W) | ΔU |
|---|---|---|---|
| Isothermal | Q = W | W = Q | ΔU = 0 |
| Adiabatic | Q = 0 | W | ΔU = -W |
| Isochoric | Q | W = 0 | ΔU = Q |
| Isobaric | Q | W = PΔV | ΔU = Q – W |
| Cyclic | Q = W | W | ΔU = 0 |
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