Complete combustion of a 0.350 g sample of a compound in a bomb calorimeter releases 14.0 kJ of heat. The bomb calorimeter has a mass of 1.20 kg and a specific heat of [tex]$3.55 J /\left( g ^{\circ} C \right)$[/tex].
If the initial temperature of the calorimeter is [tex]$22.5^{\circ} C$[/tex], what is its final temperature?
Use [tex]$q=m C_p \Delta T$[/tex].
A. [tex]$19.2^{\circ} C$[/tex]
B. [tex]$25.8^{\circ} C$[/tex]
C. [tex]$34.2^{\circ} C$[/tex]
D. [tex]$72.3^{\circ} C$[/tex]
Answer (1)
Convert the mass of the calorimeter to grams: m c a l = 1200 g .
Calculate the change in temperature: \Delta T = \frac{14000}{1200 \times 3.55} \approx 3.29 \,^{\circ}C .
Calculate the final temperature: T_{final} = 22.5 + 3.29 = 25.79 \,^{\circ}C .
The final temperature of the calorimeter is 25. 8 ∘ C .
Explanation
Problem Setup and Given Information We are given that a 0.350 g sample releases 14.0 kJ of heat when combusted in a bomb calorimeter. The calorimeter has a mass of 1.20 kg and a specific heat of 3.55 J/(g \,^{\circ}C) . The initial temperature is 22. 5 ∘ C , and we want to find the final temperature. We will use the formula q = m C p Δ T .
Convert mass of calorimeter to grams First, we need to convert the mass of the calorimeter from kg to g: m c a l = 1.20 kg × 1000 kg g = 1200 g .
Heat absorbed by calorimeter The heat released by the combustion is absorbed by the calorimeter. Thus, q = 14.0 kJ = 14000 J . We can use the formula q = m C p Δ T to find the change in temperature, Δ T .
Calculate the change in temperature \Delta T = \frac{q}{m C_p} = \frac{14000 \text{ J}}{1200 \text{ g} \times 3.55 \frac{\text{J}}{\text{g} \,^{\circ}C}} = \frac{14000}{1200 \times 3.55} \,^{\circ}C = \frac{14000}{4260} \,^{\circ}C \approx 3.29 \,^{\circ}C .
Calculate the final temperature Now, we can find the final temperature using the formula: T_{final} = T_{initial} + \Delta T = 22.5 \,^{\circ}C + 3.29 \,^{\circ}C = 25.79 \,^{\circ}C .
Final Answer Therefore, the final temperature of the calorimeter is approximately 25. 8 ∘ C .
Examples
Bomb calorimeters are used to measure the heat released during chemical reactions, such as the combustion of fuels or the digestion of foods. For example, nutritionists use bomb calorimeters to determine the caloric content of food by measuring the heat released when the food is completely burned. This information is crucial for understanding the energy provided by different foods and for designing balanced diets.
