Questions: Calculate the heat (in kJ) associated with the cooling of 363 g of mercury from 67.9°C to 12.0°C. Round your answer to 2 significant digits.

Solution Steps

We are given:

• Mass of mercury, \( m = 363 \, \text{g} \)
• Initial temperature, \( T_i = 67.9^\circ \text{C} \)
• Final temperature, \( T_f = 12.0^\circ \text{C} \)
• Specific heat capacity of mercury, \( c = 0.140 \, \text{J/g}^\circ\text{C} \)

The change in temperature, \(\Delta T\), is calculated as: \[ \Delta T = T_f - T_i = 12.0^\circ \text{C} - 67.9^\circ \text{C} = -55.9^\circ \text{C} \]

The heat change, \( q \), associated with the cooling process is given by the formula: \[ q = m \cdot c \cdot \Delta T \] Substituting the known values: \[ q = 363 \, \text{g} \times 0.140 \, \text{J/g}^\circ\text{C} \times (-55.9^\circ \text{C}) \] \[ q = 363 \times 0.140 \times (-55.9) = -2840.802 \, \text{J} \]

Convert the heat change from joules to kilojoules: \[ q = -2840.802 \, \text{J} \times \frac{1 \, \text{kJ}}{1000 \, \text{J}} = -2.8408 \, \text{kJ} \]

Round the answer to 2 significant digits: \[ q \approx -2.8 \, \text{kJ} \]

Final Answer