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Temperature Scales and Conversion
Temperature is a fundamental physical quantity that measures the average kinetic energy of particles in a substance. Different temperature scales are used around the world for various purposes.
Temperature Scales
| Scale | Symbol | Freezing Point of Water | Boiling Point of Water | Absolute Zero |
|---|---|---|---|---|
| Celsius | °C | 0°C | 100°C | -273.15°C |
| Fahrenheit | °F | 32°F | 212°F | -459.67°F |
| Kelvin | K | 273.15 K | 373.15 K | 0 K |
Celsius Scale (°C)
The Celsius scale, also called centigrade, is widely used in science and most countries worldwide. It's defined by:
- 0°C = freezing point of water at 1 atm
- 100°C = boiling point of water at 1 atm
- 100 equal divisions between these two points
Fahrenheit Scale (°F)
The Fahrenheit scale is primarily used in the United States. It was originally based on the lowest temperature achievable with a mixture of ice and salt (0°F) and human body temperature (originally 96°F, later revised to 98.6°F).
Kelvin Scale (K)
The Kelvin scale is the SI base unit for temperature and is used extensively in scientific calculations. It's an absolute temperature scale that starts at absolute zero, where all molecular motion ceases.
Key features:- No negative values (starts at 0 K)
- Same degree size as Celsius scale
- Used in gas laws, thermodynamics, and physics
- No degree symbol (just K, not °K)
Conversion Formulas
Celsius ⇔ Kelvin
\(K = °C + 273.15\)
\(°C = K - 273.15\)
Celsius ⇔ Fahrenheit
\(°F = °C \times \frac{9}{5} + 32\)
\(°C = (°F - 32) \times \frac{5}{9}\)
Kelvin ⇔ Fahrenheit
\(°F = (K - 273.15) \times \frac{9}{5} + 32\)
\(K = (°F - 32) \times \frac{5}{9} + 273.15\)
Important Temperature Values
| Description | Celsius | Fahrenheit | Kelvin |
|---|---|---|---|
| Absolute zero | -273.15°C | -459.67°F | 0 K |
| Water freezes | 0°C | 32°F | 273.15 K |
| Room temperature | 20°C | 68°F | 293.15 K |
| Human body temperature | 37°C | 98.6°F | 310.15 K |
| Water boils | 100°C | 212°F | 373.15 K |
Solved Examples
Example 1: A fever thermometer reads 39°C. What is this temperature in Fahrenheit?
Step 1: Identify the conversion formula: \(°F = °C \times \frac{9}{5} + 32\)
Step 2: Substitute the values: \(°F = 39 \times \frac{9}{5} + 32\)
Step 3: Calculate: \(°F = 39 \times 1.8 + 32 = 70.2 + 32 = 102.2°F\)
Result: 39°C = 102.2°F (high fever temperature)
Example 2: The weather forecast shows 86°F. What is this temperature in Celsius?
Step 1: Identify the conversion formula: \(°C = (°F - 32) \times \frac{5}{9}\)
Step 2: Substitute the values: \(°C = (86 - 32) \times \frac{5}{9}\)
Step 3: Calculate: \(°C = 54 \times \frac{5}{9} = 54 \times 0.556 = 30°C\)
Result: 86°F = 30°C (hot summer day)
Example 3: Liquid nitrogen has a boiling point of 77.36 K. What is this temperature in Celsius?
Step 1: Identify the conversion formula: \(°C = K - 273.15\)
Step 2: Substitute the values: \(°C = 77.36 - 273.15\)
Step 3: Calculate: \(°C = -195.79°C\)
Result: 77.36 K = -195.79°C (extremely cold!)
Example 4: At what temperature do the Celsius and Fahrenheit scales show the same numerical value?
Step 1: Set up the equation. Let x be the temperature where °C = °F: \(x = x \times \frac{9}{5} + 32\)
Step 2: Solve for x: \(x = \frac{9x}{5} + 32\)
\(x - \frac{9x}{5} = 32\)
\( \frac{5x - 9x}{5} = 32\)
\( \frac{-4x}{5} = 32\)
\(x = 32 \times \frac{-5}{4} = -40\)
Result: -40°C = -40°F (the only point where both scales are equal)
Example 5: A gas is heated from 25°C to 150°F. What is the temperature change in Kelvin?
Step 1: Convert initial temperature to Kelvin: \(T_1 = 25°C + 273.15 = 298.15 \text{ K}\)
Step 2: Convert final temperature to Kelvin. First convert 150°F to Celsius: \(°C = (150 - 32) \times \frac{5}{9} = 118 \times \frac{5}{9} = 65.56°C\)
Then convert to Kelvin: \(T_2 = 65.56°C + 273.15 = 338.71 \text{ K}\)
Step 3: Calculate temperature change: \(\Delta T = T_2 - T_1 = 338.71 - 298.15 = 40.56 \text{ K}\)
Result: The temperature increased by 40.56 K
Example 6: The surface temperature of the Sun is approximately 5778 K. Express this in Celsius and Fahrenheit.
Step 1: Convert to Celsius: \(°C = K - 273.15 = 5778 - 273.15 = 5504.85°C\)
Step 2: Convert to Fahrenheit: \(°F = °C \times \frac{9}{5} + 32 = 5504.85 \times \frac{9}{5} + 32 = 9908.73 + 32 = 9940.73°F\)
Result: Sun's surface temperature is 5505°C or 9941°F
Scientific notation: This is approximately 5.78 × 10³ K, 5.50 × 10³ °C, or 9.94 × 10³ °F