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What is the specific heat of lead if it takes 97.4 J to raise the temperature of a 75.3 g block by 10.2 °C?

Express your answer with the appropriate units.

Specific heat = ______ Value ______ Units

Answer :

To find the specific heat of lead, we use the formula for specific heat capacity:

[tex]\[ \text{specific heat} (c) = \frac{\text{energy added (Q)}}{\text{mass (m)} \times \text{temperature change } (\Delta T)} \][/tex]

Given:
- Energy added (Q) = 97.4 J
- Mass (m) = 75.3 g
- Temperature change ([tex]\(\Delta T\)[/tex]) = 10.2 °C

We plug these values into the formula:

[tex]\[ c = \frac{97.4 \, \text{J}}{75.3 \, \text{g} \times 10.2 \, °\text{C}} \][/tex]

Calculating the denominator:

[tex]\[ 75.3 \, \text{g} \times 10.2 \, °\text{C} = 768.06 \, \text{g°C} \][/tex]

Now, calculate the specific heat:

[tex]\[ c = \frac{97.4 \, \text{J}}{768.06 \, \text{g°C}} \approx 0.1268 \, \text{J/g°C} \][/tex]

So, the specific heat of lead is approximately [tex]\(0.1268 \, \text{J/g°C}\)[/tex].

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