Questions: Calculate the energy required to heat 501.0 g of graphite from 7.9°C to 19.3°C. Assume the specific heat capacity of graphite under these conditions is 0.710 J · g^-1 · K^-1. Round your answer to 3 significant digits.

Calculate the energy required to heat 501.0 g of graphite from 7.9°C to 19.3°C. Assume the specific heat capacity of graphite under these conditions is 0.710 J · g^-1 · K^-1. Round your answer to 3 significant digits.

Transcript text: Calculate the energy required to heat 501.0 g of graphite from $7.9{ }^{\circ} \mathrm{C}$ to $19.3^{\circ} \mathrm{C}$. Assume the specific heat capacity of graphite under these conditions is $0.710 \mathrm{~J} \cdot \mathrm{~g}^{-1} \cdot \mathrm{~K}^{-1}$. Round your answer to 3 significant digits.

Solution

Solution Steps

Step 1: Identify the Given Values

We are given the following values:

Mass of graphite, $ m = 501.0 \, \text{g} $
Initial temperature, $ T_i = 7.9^\circ \text{C} $
Final temperature, $ T_f = 19.3^\circ \text{C} $
Specific heat capacity of graphite, $ c = 0.710 \, \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} $

Step 2: Calculate the Temperature Change

The change in temperature, $\Delta T$, is calculated as follows: \[ \Delta T = T_f - T_i = 19.3^\circ \text{C} - 7.9^\circ \text{C} = 11.4 \, \text{K} \]

Step 3: Use the Formula for Heat Energy

The formula to calculate the heat energy required is: \[ q = m \cdot c \cdot \Delta T \] Substituting the given values: \[ q = 501.0 \, \text{g} \times 0.710 \, \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} \times 11.4 \, \text{K} \]

Step 4: Perform the Calculation

Calculate the energy: \[ q = 501.0 \times 0.710 \times 11.4 = 4053.294 \, \text{J} \]

Step 5: Round the Answer

Round the result to 3 significant digits: \[ q \approx 4050 \, \text{J} \]