Questions: 5. What would be the temperature change of a 24.2 g sample of carbon if 575.6 J of heat energy was applied?

Solution Steps

The specific heat capacity (\(c\)) of carbon is a known value. For carbon, \(c = 0.709 \, \text{J/g°C}\).

The formula to calculate the temperature change (\(\Delta T\)) when heat energy is applied is:

\[ q = mc\Delta T \]

where:

• \(q\) is the heat energy applied (575.6 J),
• \(m\) is the mass of the sample (24.2 g),
• \(c\) is the specific heat capacity (0.709 J/g°C),
• \(\Delta T\) is the temperature change.

Rearrange the formula to solve for \(\Delta T\):

\[ \Delta T = \frac{q}{mc} \]

Substitute the known values into the equation:

\[ \Delta T = \frac{575.6 \, \text{J}}{24.2 \, \text{g} \times 0.709 \, \text{J/g°C}} \]

Calculate \(\Delta T\):

\[ \Delta T = \frac{575.6}{17.1618} \approx 33.54 \, \text{°C} \]

Final Answer