Thermal Experiments

Thermal experiments physics aur engineering me heat transfer, temperature measurement, specific heat, thermal expansion, and calorimetry ko study karne ke liye kiye jate hain. Ye experiments fundamental thermodynamics principles ko practically demonstrate karte hain aur students, researchers, aur engineers ke liye conceptual understanding aur skill development me madadgar hote hain.

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1. Introduction

Thermal Physics:

Study of heat, temperature, energy transfer, and properties of matter under thermal influence.

Importance of Thermal Experiments:

1. Understanding specific heat and latent heat
2. Measuring thermal conductivity
3. Studying thermal expansion of solids and liquids
4. Calorimetry applications in chemical reactions and materials testing
5. Understanding laws of thermodynamics practically

Key Quantities Measured:

• Temperature (T)
• Heat (Q)
• Thermal expansion (ΔL, ΔV)
• Specific heat (c)
• Latent heat (L)

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2. Measurement of Temperature

2.1 Thermometers

1. Mercury-in-glass thermometer
   • Principle: Thermal expansion of mercury
   • Range: –39°C to 356°C
   • Applications: Laboratory, weather, industry
2. Alcohol thermometer
   • Principle: Thermal expansion of alcohol
   • Low freezing point – for very cold environments
3. Thermocouples
   • Based on Seebeck effect
   • Measures wide range of temperatures
   • Used in furnaces, engines, and industry
4. Thermistors and RTDs
   • Electrical resistance changes with temperature
   • High precision measurement in labs

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2.2 Experimental Considerations

• Immersion depth of thermometer
• Avoiding heat loss to surroundings
• Calibrating thermometer against standard ice and steam points

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3. Specific Heat Determination

Specific Heat (c):

Amount of heat required to raise the temperature of 1 kg of substance by 1°C.

Q=mcΔTQ = m c \Delta TQ=mcΔT

3.1 Method: Calorimetry

• Apparatus: Calorimeter, thermometer, heater, stirrer
• Procedure:
  1. Measure mass of substance mmm and water mwm_wmw​ in calorimeter
  2. Heat substance to known temperature TsT_sTs​
  3. Immerse in water (initial temperature TwT_wTw​)
  4. Measure final equilibrium temperature TfT_fTf​
• Energy balance:

mcs(Ts−Tf)=mwcw(Tf−Tw)m c_s (T_s – T_f) = m_w c_w (T_f – T_w)mcs​(Ts​−Tf​)=mw​cw​(Tf​−Tw​)

• Solve for csc_scs​

3.2 Errors and Precautions

• Heat loss to surroundings
• Imperfect insulation
• Stirring ensures uniform temperature

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4. Latent Heat Measurement

Latent Heat (L):

Heat absorbed or released during phase change without temperature change.

Q=mLQ = m LQ=mL

4.1 Method: Calorimeter Method

• Ice melting in calorimeter
• Mass of water and ice measured
• Temperature changes recorded
• Energy balance:

miL=(mwcw+mccc)(Tf−Tw)m_i L = (m_w c_w + m_c c_c)(T_f – T_w)mi​L=(mw​cw​+mc​cc​)(Tf​−Tw​)

Where mcm_cmc​ = mass of calorimeter, ccc_ccc​ = specific heat of calorimeter

4.2 Applications

• Determining latent heat of fusion of ice
• Steam condensation calorimetry
• Material property testing

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5. Thermal Expansion Experiments

5.1 Linear Expansion of Solids

ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta TΔL=αL0​ΔT

• α\alphaα = coefficient of linear expansion
• Apparatus: Metal rod, vernier scale, heater or water bath
• Procedure:
  1. Measure initial length L0L_0L0​
  2. Heat rod by ΔT\Delta TΔT
  3. Measure length increase ΔL\Delta LΔL
• Plot ΔL vs ΔT → slope gives α

5.2 Volumetric Expansion of Liquids

ΔV=βV0ΔT\Delta V = \beta V_0 \Delta TΔV=βV0​ΔT

• Apparatus: Flask with liquid, thermometer, burette
• Measure volume change with temperature
• Applications: Thermometers, expansion joints, fluid flow

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6. Thermal Conductivity Measurement

Thermal Conductivity (k):

Rate of heat transfer through material per unit area per unit temperature gradient.

6.1 Method: Lee’s Disc Method

• Metal disc heated, placed on insulating disc
• Measure temperature difference over time
• Formula:

k=QLAΔTtk = \frac{Q L}{A \Delta T t}k=AΔTtQL​

• Applications: Insulation design, material testing

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7. Heat Transfer Experiments

7.1 Conduction

• Apparatus: Metal rod with heater and thermocouples
• Measure temperature gradient along rod
• Fourier’s law:

Qt=−kAdTdx\frac{Q}{t} = – k A \frac{dT}{dx}tQ​=−kAdxdT​

7.2 Convection

• Measure heat transfer in liquids with heater and thermometer
• Natural convection: Due to density difference
• Forced convection: Using fan or pump

7.3 Radiation

• Stefan-Boltzmann law:

P=σϵAT4P = \sigma \epsilon A T^4P=σϵAT4

• Measure heat emitted by blackbody surface

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8. Calorimeter Experiment – Detailed Procedure

1. Initial Measurements: Mass of water and calorimeter, initial temperatures
2. Add hot object or ice: Record final equilibrium temperature
3. Calculate heat exchange:

Qlost=QgainedQ_{lost} = Q_{gained}Qlost​=Qgained​

4. Determine unknown quantity: Specific heat or latent heat

8.1 Error Analysis

• Heat loss to environment
• Non-uniform temperature distribution
• Instrument calibration

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9. Experimental Determination of Thermal Expansion Coefficient

• Linear Expansion: α=ΔLL0ΔT\alpha = \frac{\Delta L}{L_0 \Delta T}α=L0​ΔTΔL​
• Volumetric Expansion: β=ΔVV0ΔT\beta = \frac{\Delta V}{V_0 \Delta T}β=V0​ΔTΔV​
• Precision instruments: Micrometer screw, Vernier calipers, thermometers

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10. Practical Applications of Thermal Experiments

1. Design of heat exchangers
2. Engineering materials testing
3. Thermal insulation in buildings
4. Manufacturing and metallurgy
5. Thermodynamics research and chemical process optimization

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11. Numerical Examples

Example 1: Specific Heat Determination

• Mass of metal: 200 g, heated to 100°C
• Water: 300 g at 25°C, final temperature: 30°C

mc(Ts−Tf)=mwcw(Tf−Tw)m c (T_s – T_f) = m_w c_w (T_f – T_w)mc(Ts​−Tf​)=mw​cw​(Tf​−Tw​) 0.2c(100−30)=0.3⋅4200⋅(30−25)0.2 c (100 – 30) = 0.3 \cdot 4200 \cdot (30 – 25)0.2c(100−30)=0.3⋅4200⋅(30−25) 0.2c⋅70=0.3⋅4200⋅50.2 c \cdot 70 = 0.3 \cdot 4200 \cdot 50.2c⋅70=0.3⋅4200⋅5 c=450J/kg°Cc = 450 J/kg°Cc=450J/kg°C

Example 2: Linear Expansion

• Rod: L0=1mL_0 = 1 mL0​=1m, ΔT = 50°C, α = 1.2 ×10⁻⁵ /°C

ΔL=αL0ΔT=1.2×10−5⋅1⋅50=0.0006m=0.6mm\Delta L = \alpha L_0 \Delta T = 1.2 \times 10^{-5} \cdot 1 \cdot 50 = 0.0006 m = 0.6 mmΔL=αL0​ΔT=1.2×10−5⋅1⋅50=0.0006m=0.6mm

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12. Summary Table

Experiment	Quantity Measured	Formula / Relation	Instrument
Specific Heat of Solids	c (J/kg°C)	Q=mcΔTQ = mc \Delta TQ=mcΔT	Calorimeter
Latent Heat of Ice	L (J/kg)	Q=mLQ = m LQ=mL	Calorimeter
Linear Expansion of Rod	α (1/°C)	ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta TΔL=αL0​ΔT	Vernier/Micrometer
Volumetric Expansion of Liquid	β (1/°C)	ΔV=βV0ΔT\Delta V = \beta V_0 \Delta TΔV=βV0​ΔT	Burette/Flask
Thermal Conductivity	k (W/m·K)	Qt=kAΔTL\frac{Q}{t} = k A \frac{\Delta T}{L}tQ​=kALΔT​	Lee’s disc/rod
Heat Transfer (Radiation)	P (W)	P=σϵAT4P = \sigma \epsilon A T^4P=σϵAT4	Blackbody setup