define and use specific heat capacity

Temperature Scales

📚 What is a temperature scale? It’s a way to give a number to how hot or cold something is. In physics we mainly use three scales: Celsius (°C), Kelvin (K) and Fahrenheit (°F). Each has its own reference points and uses.

Celsius (°C)

❄️ Reference points: 0 °C = freezing point of water, 100 °C = boiling point of water (at 1 atm). 🔢 Scale spacing: 1 °C = 1 °C (same size as Kelvin, but offset).

Fahrenheit (°F)

❄️ Reference points: 32 °F = freezing point of water, 212 °F = boiling point of water. 🔢 Scale spacing: 1 °F = 5/9 °C (≈0.555 °C). 📌 Tip: Remember the “32‑212” trick: add 32 to get °F, subtract 32 and multiply by 5/9 to get °C.

Kelvin (K)

❄️ Reference point: 0 K = absolute zero (no thermal motion). 🔢 Scale spacing: 1 K = 1 °C (same size, just shifted). 📌 Why Kelvin? It’s the SI unit for temperature, so all physics equations use Kelvin.

Specific Heat Capacity

🔬 Definition: The amount of heat energy needed to raise the temperature of 1 kg of a substance by 1 °C (or 1 K). Symbol: $c$.

Why is it useful?

🧊 Example: Water has a high specific heat ($c_{\text{water}} \approx 4.18 \,\text{J g}^{-1}\text{°C}^{-1}$). That’s why a cup of hot coffee cools slowly – the water can absorb a lot of heat before its temperature rises.

Heat Energy Formula

The basic equation: $$q = mc\Delta T$$ where:

• $q$ = heat energy (J)
• $m$ = mass (kg)
• $c$ = specific heat capacity (J kg⁻¹ K⁻¹)
• $\Delta T$ = change in temperature (K or °C)

Practical Example

🔢 Problem: How much heat is required to raise 500 g of water from 20 °C to 80 °C?

1. Convert mass to kg: $m = 0.5\,\text{kg}$
2. Find $\Delta T = 80 - 20 = 60\,\text{K}$
3. Use $c_{\text{water}} = 4180\,\text{J kg}^{-1}\text{K}^{-1}$
4. Compute: $q = 0.5 \times 4180 \times 60 \approx 1.25 \times 10^5\,\text{J}$

Specific Heat Capacity Table

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