Phase Diagram Interpretation and Thermochemistry

Q11. What is the specific heat of silicon if the temperature of a 4.11 g sample of silicon is increased by 3.8°C when 11.1 J of heat is added?

Background

Topic: Thermochemistry – Specific Heat Capacity

This question tests your understanding of how to calculate the specific heat capacity of a substance using the relationship between heat, mass, temperature change, and specific heat.

Key formula:

$q = m \; c_s \; \Delta T$

Where:

• $q$ = heat absorbed (in Joules)

• $m$ = mass of the sample (in grams)

• $c_s$ = specific heat capacity (in J/g°C)

• $\Delta T$ = change in temperature (in °C)

Step-by-Step Guidance

1. Identify the known values: $q = 11.1$ J, $m = 4.11$ g, $\Delta T = 3.8$ °C.

2. Write the formula for specific heat: $q = m \; c_s \; \Delta T$.

3. Rearrange the formula to solve for $c_s$: $c_s = \frac{q}{m \; \Delta T}$.

4. Set up the calculation by plugging in the values, but do not compute the final result yet.

Try solving on your own before revealing the answer!

Final Answer: 0.71 J/g°C

$c_s = \frac{11.1}{4.11 \times 3.8} \approx 0.71$ J/g°C

The specific heat tells you how much energy is needed to raise 1 gram of silicon by 1°C. Here, the calculation shows silicon's specific heat is 0.71 J/g°C.