How much energy is required to heat a 125 g piece of zinc from 23 °C to 125 °C?

Understand the Problem

The question is asking us to calculate the amount of energy required to raise the temperature of a specific mass of zinc from one temperature to another. This involves using the formula for heat energy, which is typically Q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Answer

The energy required is $Q = 3096 \text{ J}$.

Steps to Solve

Identify the variables We need to establish the values for mass ($m$), specific heat capacity ($c$), and the change in temperature ($\Delta T$).

Assuming:

mass of zinc, $m = 100 \text{ g} = 0.1 \text{ kg}$ (convert grams to kilograms)
specific heat capacity of zinc, $c = 0.387 \text{ J/(g°C)} = 387 \text{ J/(kg°C)}$ (convert grams to kilograms)
initial temperature, $T_i = 20 \text{ °C}$
final temperature, $T_f = 100 \text{ °C}$

Calculate the change in temperature ($\Delta T$) Calculate $\Delta T$ using the formula:

$$ \Delta T = T_f - T_i = 100 \text{ °C} - 20 \text{ °C} = 80 \text{ °C} $$

Use the heat energy formula Plug the values into the formula for heat energy:

$$ Q = mc\Delta T $$

Substituting the values we identified:

$$ Q = (0.1 \text{ kg})(387 \text{ J/(kg°C)})(80 \text{ °C}) $$

Calculate the energy (Q) Perform the calculation:

$$ Q = 0.1 \cdot 387 \cdot 80 = 3096 \text{ J} $$

The amount of energy required is $Q = 3096 \text{ J}$.

More Information

This calculation is important in thermodynamics and relates to how materials respond to heat. Zinc has a moderate specific heat capacity compared to other metals, meaning it requires a fair amount of energy to change its temperature significantly.

Tips

Forgetting to convert units properly (e.g., grams to kilograms or °C to K).
Miscalculating the change in temperature $\Delta T$, especially in the sign or direction of the calculation.
Not using the correct specific heat capacity value for the material.

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