Question

10. The specific heat of iron is 0.452 J/g * C. How much heat is released when 255g of iron cools from 90 degrees Celsius to 50 degrees Celsius? Show your work.

Answer 1

To calculate the heat released when the iron cools down, we can use the formula for heat transfer:

\[
q = mc\Delta T
\]

where:
- \( q \) = heat transfer (in Joules)
- \( m \) = mass of the substance (in grams)
- \( c \) = specific heat capacity (in J/g°C)
- \( \Delta T \) = change in temperature (in °C)

Here are the variables we have:
- \( m = 255 \text{ g} \)
- \( c = 0.452 \text{ J/g°C} \)
- The initial temperature \( T_i = 90°C \)
- The final temperature \( T_f = 50°C \)

First, we need to calculate \( \Delta T \):

\[
\Delta T = T_f - T_i = 50°C - 90°C = -40°C
\]

(Note that \( \Delta T \) is negative because the temperature is decreasing.)

Now we can plug in the values into the heat transfer formula:

\[
q = mc\Delta T
\]

Substituting in the values:

\[
q = 255 \text{ g} \times 0.452 \text{ J/g°C} \times (-40°C)
\]

Calculating \( q \):

\[
q = 255 \times 0.452 \times (-40)
\]
\[
q = 255 \times 0.452 \times -40 = 255 \times -18.08 = -4610.4 \text{ J}
\]

Thus, the heat released when 255 g of iron cools from 90°C to 50°C is approximately:

\[
\boxed{-4610.4 \text{ J}}
\]

The negative sign indicates that heat is being released.