Heat and Thermometer REvision Notes BTER Polytechnic Classes

 

Heat and Thermometry

Heat and temperature are fundamental concepts in thermodynamics, physics, and engineering. This chapter focuses on understanding the basic principles of heat transfer, temperature measurement, and thermometry.

---

5.1 Concept of Heat and Temperature

1. Heat:

   • Definition: Heat is a form of energy that is transferred between systems or objects due to a temperature difference. It always flows from the body with higher temperature to the body with lower temperature.
   • Unit: The SI unit of heat is the Joule (J). Other units like calorie are also used in some contexts ($1 \, \text{cal} = 4.18 \, \text{J}$).

2. Temperature:

   • Definition: Temperature is a measure of the average kinetic energy of the molecules in a substance. It determines the direction of heat flow and is an indicator of how hot or cold an object is.
   • Unit: The SI unit of temperature is the Kelvin (K). Other units include Celsius (°C) and Fahrenheit (°F).

---

5.2 Modes of Heat Transfer

Heat transfer occurs through three main modes: conduction, convection, and radiation. Each mode involves different mechanisms of energy flow.

1. Conduction:

• Definition: Conduction is the process of heat transfer through a material without the movement of the material itself. It occurs when particles of the material vibrate or move, transferring kinetic energy to adjacent particles.
• Example: Heating one end of a metal rod causes the heat to travel to the other end by conduction.
• Thermal Conductivity: The rate of heat transfer by conduction depends on the material’s thermal conductivity ($k$), which varies for different materials. The formula is: $$Q = \frac{kA(T_1 - T_2)}{L}$$ Where:
  • $Q$ is the heat transferred (in joules, J),
  • $k$ is the thermal conductivity (W/m·K),
  • $A$ is the cross-sectional area (m²),
  • $(T_1 - T_2)$ is the temperature difference (K or °C),
  • $L$ is the length of the material (m).

2. Convection:

• Definition: Convection is the transfer of heat by the physical movement of fluid (liquid or gas). The heated fluid rises and cooler fluid moves in to take its place, setting up a circulating flow.
• Example: The heating of water in a pot, where hot water rises and cooler water moves down.
• Formula for Heat Transfer Rate: $$Q = hA(T_s - T_\infty)$$ Where:
  • $Q$ is the heat transferred (W),
  • $h$ is the convective heat transfer coefficient (W/m²·K),
  • $A$ is the surface area (m²),
  • $T_s$ is the surface temperature (°C or K),
  • $T_\infty$ is the ambient temperature (°C or K).

3. Radiation:

• Definition: Radiation is the transfer of heat through electromagnetic waves, without the need for a medium. It occurs at all temperatures and is responsible for the heat from the Sun reaching the Earth.
• Example: The warmth felt when standing near a fire or under sunlight.
• Stefan-Boltzmann Law: $$Q = \sigma A \epsilon (T^4 - T_0^4)$$ Where:
  • $Q$ is the heat radiated (W),
  • $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \, \text{W/m}^2\cdot K^4$),
  • $A$ is the surface area (m²),
  • $\epsilon$ is the emissivity of the material (a value between 0 and 1),
  • $T$ is the temperature of the body (K),
  • $T_0$ is the temperature of the surroundings (K).

---

5.3 Newton’s Law of Cooling

• Statement: Newton’s Law of Cooling states that the rate of change of temperature of an object is directly proportional to the difference between the temperature of the object and the ambient temperature, provided the temperature difference is small.

  $$\frac{dT}{dt} = -k(T - T_\text{ambient})$$

  Where:

  • $\frac{dT}{dt}$ is the rate of change of temperature of the object,
  • $T$ is the temperature of the object,
  • $T_\text{ambient}$ is the temperature of the surroundings,
  • $k$ is the constant of proportionality.

• This law applies to cooling processes like a cup of hot coffee cooling down in the air.

---

5.4 Scales of Temperature and Their Relationship

Temperature can be measured using different scales, the most common being Celsius, Fahrenheit, and Kelvin. The relationship between these scales is as follows:

• Celsius to Kelvin: $$T(K) = T(°C) + 273.15$$
• Celsius to Fahrenheit: $$T(°F) = \frac{9}{5} T(°C) + 32$$
• Fahrenheit to Kelvin: $$T(K) = \frac{5}{9} (T(°F) - 32) + 273.15$$

---

5.5 Types of Thermometers and Their Uses

Thermometers are instruments used to measure temperature. Different types of thermometers operate based on different principles, including thermal expansion, electrical resistance, and radiation.

1. Mercury Thermometer:

• Principle: This thermometer uses mercury, which expands and contracts with temperature changes, to indicate the temperature on a scale.
• Uses: Commonly used in laboratories, weather stations, and medical applications to measure temperature.
• Limitation: Mercury thermometers are fragile and are less useful at extreme temperatures.

2. Platinum Resistance Thermometer (PRT):

• Principle: This thermometer works by measuring the change in resistance of a platinum wire with temperature. As temperature increases, the resistance of the platinum increases in a nearly linear fashion.
• Uses: Used in precise industrial applications, scientific experiments, and temperature calibration due to its high accuracy.
• Limitation: More expensive and less portable than mercury thermometers.

3. Pyrometer:

• Principle: A pyrometer measures temperature by detecting the radiation emitted by an object. It is often used for very high-temperature measurements, especially in industrial settings.
• Uses: Typically used for measuring the temperature of molten metals, furnaces, and other objects in extreme temperature conditions.
• Types:
  • Optical Pyrometer: Measures temperature based on the visible radiation emitted by an object.
  • Infrared Pyrometer: Measures temperature using infrared radiation.
• Limitation: They can only measure the temperature of an object without contact and are generally used for high temperatures.

---

Summary of Key Concepts:

1. Heat vs. Temperature: Heat is energy transferred due to a temperature difference, while temperature is a measure of the average kinetic energy of particles in a substance.
2. Modes of Heat Transfer:
   • Conduction: Heat transfer through direct contact.
   • Convection: Heat transfer through fluid motion.
   • Radiation: Heat transfer through electromagnetic waves.
3. Newton’s Law of Cooling: States that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings.
4. Temperature Scales: Celsius, Fahrenheit, and Kelvin are commonly used temperature scales, and they are interrelated by simple formulas.
5. Types of Thermometers:
   • Mercury Thermometer: Based on the expansion of mercury.
   • Platinum Resistance Thermometer: Uses resistance of platinum to measure temperature.
   • Pyrometer: Measures temperature based on the radiation emitted by an object.

These concepts and instruments are crucial for accurate temperature measurement and for understanding heat transfer processes in various applications in science and engineering.