Temperature and Heat - Comprehensive Notes

Temperature and Heat

Temperature Measurement

• Temperature is measured using a thermometer.

• Thermometers utilize the principle that materials expand with increasing temperature.

• Example: Mercury thermometer

  • A mercury-filled glass bulb connected to a capillary tube.

  • When heated, mercury expands into the capillary tube.

  • The expansion amount is proportional to the change in temperature.

  • The glass is marked with a scale for reading the temperature.

Temperature Scales

• Common temperature scales: Fahrenheit (°F) and Celsius (°C).

• Freezing point of water:

  • 0°C

  • 32°F

• Boiling point of water:

  • 100°C

  • 212°F

• Celsius scale:

  • 100 degrees between ice and steam points.

• Fahrenheit scale:

  • 180 degrees between ice and steam points.

• Each Celsius degree is larger than each Fahrenheit degree by a factor of 9/5.

Conversion Formula

• $T(°F) = \frac{9}{5} T(°C) + 32$

Example

• A healthy person has an oral temperature of 98.6°F.

Kelvin Temperature Scale

• The Kelvin scale is scientifically significant.

• The symbol for Kelvin is K (without a degree sign).

• Example: 300 K (not 300 °K).

• 100 divisions between ice and steam points on both Kelvin and Celsius scales.

• The size of one Kelvin is identical to the size of one Celsius degree.

• Ice point (0°C) occurs at 273.15 K.

Kelvin to Celsius Conversion

• $T(K) = T(°C) + 273.15$

• The number 273.15 is an experimental result.

Absolute Zero

• Lowest possible temperature.

• Defined as the zero point on the Kelvin scale.

Pressure

• $P = \frac{F}{A}$

  • P: Pressure.

  • F: Force acting perpendicular to a surface.

  • A: Area over which the force acts.

• Pressure is a scalar quantity.

• When a gas confined to a fixed volume is heated, its pressure increases.

• Pressure-versus-temperature graph yields a straight line.

Extrapolation to Absolute Zero

• Extrapolating the pressure-versus-temperature line crosses the temperature axis at -273.15°C.

• Gases liquefy before reaching this temperature.

• Helium and hydrogen are used in thermometers due to their low liquefaction temperatures.

• The absolute zero point (-273.15°C) has fundamental significance.

• Temperatures lower than -273.15°C cannot be reached.

• Negative absolute gas pressure has no physical meaning.

• The Kelvin scale's absolute zero is the lowest attainable temperature.

Thermal Expansion

• Most materials expand when heated and contract when cooled.

Types of Thermal Expansion

• Linear Thermal Expansion

  • Expansion in one dimension (e.g., length).

  • Occurs in solids.

• Volume Thermal Expansion

  • Expansion in all three dimensions.

  • Occurs in solids, liquids, and gases.

Real-World Example

• Metal lid on a glass jar: Heating the lid with hot water loosens it because the metal expands more than the glass.

• Different materials expand at different rates when heated to the same temperature.

Linear Thermal Expansion Formula

• Let the initial length and temperature of a rod be $L<em>0$ and $T</em>0$ respectively.

• When the temperature increases by $\Delta T$, the new temperature is $T<em>{final} = T</em>0 + \Delta T$.

• The length expands by $\Delta L$, and the new length is $L<em>{final} = L</em>0 + \Delta L$.

• Conversely, if the temperature decreases by $\Delta T$, the length decreases to $L_0 - \Delta L$.

• Change in the length of the rod: $\Delta L = L - L<em>0 = \alpha L</em>0 \Delta T$

• Temperature must be in °C.

• Length and change in length must be in meters.

• $\alpha$: Coefficient of linear expansion (Unit: °C⁻¹).

• It is a constant, depending on the material of the rod.

• Higher the value of $\alpha$, faster the object expands/contracts along its length when heated/cooled.

Expansion of Holes

• A hole in a solid material expands when heated and contracts when cooled, as if it were filled with the surrounding material.

Volume Thermal Expansion

• Relevant for liquids and gases, as well as solids.

• $\beta$: Coefficient of volume expansion.

• For uniform solids, $\beta ≈ 3\alpha$

• Higher the value of $\beta$, faster the object undergoes volume expansion/contraction when heated/cooled.

Volume Expansion Values for Materials:

• Quartz: $10^{-5}$

• Glass: $10^{-4}$

• Hg: $10^{-4}$

• Air: $10^{-3}$

• Steel: $10^{-5}$

• Al: $10^{-5}$

Question 2

• You want to take apart a couple of aluminum parts held together by steel screws, but the screws are stuck. What should you do?

• A. heat the thing up

• B. cool the thing down

• C. blow the thing up