Units of Measurement: Temperature and Energy

Units of Measurement

Temperature

• Units of Temperature:

  • U.S. Customary Unit: Degrees Fahrenheit (°F)

  • Metric System: Celsius (°C) or Centigrade

  • SI Unit (International System of Units): Kelvin (K)

Key Temperatures Related to Water:

• Freezing Point of Water:

  • Fahrenheit: 32°F

  • Celsius: 0°C

• Boiling Point of Water:

  • Fahrenheit: 212°F

  • Celsius: 100°C

Comparison of Temperature Scales:

• The Celsius scale was defined based on the freezing and boiling points of water:

  • 100 degrees Celsius between the freezing (0°C) and boiling (100°C) points of water.

• The difference between the boiling and freezing points in Fahrenheit is 180°F, while in Celsius it is 100°C, making:

  • 1°C ≈ 1.8°F.

Kelvin Scale:

• Temperature Conversion: To convert Celsius to Kelvin, the formula is:
  $(K = °C + 273)$

• Key Point: All Kelvin values are positive, with 0 K as absolute zero (−273°C).

Energy and Heat

• Definition of Calorie:

  • A calorie is the amount of energy required to raise the temperature of 1 gram of water by 1°C.

  • Example:

  • Starting with 1 gram of water at 14°C, raising it to 15°C requires 1 calorie of energy.

Comparison of Water and Copper:

• When heating 1 gram of copper (also starting at 14°C) with 1 calorie of energy, the final temperature will exceed 15°C considerably.

• Specific Heat: The specific heat of a substance indicates how readily it will heat up when energy is applied.

  • For water: 1 calorie/g°C

  • For copper: 0.092 calories/g°C

Specific Heat

• Definition: The specific heat of a substance is the amount of heat needed to raise the temperature of exactly 1 gram of that substance by exactly 1°C.

• The specific heat varies per material (water, copper, etc.) and serves as a conversion factor to connect energy (heat) to temperature changes.

• Uses of Specific Heat:

  • If a mass (m) of a substance with a specific heat (C) is heated and experiences a temperature change (ΔT), the heat (Q) added can be calculated using the formula:
    $(Q = m imes C imes ΔT)$

Example Calculation with Water:

• Situation: Heating 1000 grams of water from 20°C to 50°C.

• Specific Heat of Water: 1 calorie/g°C.

• Temperature Change: 30°C.

• Calculation:

  • $Q = 1000 ext{ g} imes 1 ext{ calorie/g°C} imes 30°C = 30,000 ext{ calories}$

Calorimetry

• Definition: Calorimetry is a process for measuring the amount of heat energy contained in a substance.

• Example: Measuring calories in a half bagel using a calorimeter:

  • Components:

  • Chamber containing oxygen and ignition wires to burn the bagel.

  • Surrounding water to absorb heat and measure temperature change.

  • Calculation Steps:

  1. Measure initial water temperature.

  2. Ignite the bagel; measure final water temperature.

  3. Calculate the temperature change (ΔT) of the water.

  4. Use the equation $Q = m imes C imes ΔT$ to find calories released by the bagel.

Example Calculation of a Bagel:

• Given Data:

  • Mass of water = 1000 g,

  • Initial Temperature = 22°C,

  • Final Temperature = 92°C,

  • Specific Heat of Water = 1 calorie/g°C.

• Temperature Change:

  • $ΔT = 92°C - 22°C = 70°C$.

• Calories Released:

  • $Q = 1000 g imes 1 ext{ calorie/g°C} imes 70°C = 70,000 ext{ calories}$.

Nutritional Calories vs. Scientific Calories:

• Nutritional Calorie: 1 nutritional calorie (Cal) = 1000 scientific calories (cal) = 1 kilocalorie (kcal).

• Example: 70,000 calories = 70 nutritional calories or 70 kilocalories.

Energy Content of Food:

• Nutritional Values per Gram:

  • Carbohydrates: 4 kcal/g

  • Proteins: 4 kcal/g

  • Fats: 9 kcal/g (Fats provide the most energy per gram.)

• Example Calculation from Whole Milk:

  • 12 g carbohydrates: $12 g imes 4 ext{ kcal/g} = 48 ext{ kcal}$

  • 9 g fat: $9 g imes 9 ext{ kcal/g} = 81 ext{ kcal}$

  • 9 g protein: $9 g imes 4 ext{ kcal/g} = 36 ext{ kcal}$

  • Total Calories: 48 + 81 + 36 = 165 kcal, matching food label data.