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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 3.55 J/(g·°C).

If the initial temperature of the calorimeter is 22.5°C, what is its final temperature?

Use [tex]\( q = m C_p \Delta T \)[/tex].

A. 19.2°C
B. 25.8°C
C. 34.2°C
D. 72.3°C

Sagot :

To determine the final temperature of the bomb calorimeter, we need to follow these steps:

1. Identify the given values:
- Initial temperature of the calorimeter, [tex]\( T_{\text{initial}} = 22.5^\circ C \)[/tex]
- Mass of the calorimeter, [tex]\( m = 1.20 \, \text{kg} \)[/tex]
- Convert the mass from kilograms to grams, since the specific heat is given in J/(g*°C):
[tex]\[ m = 1.20 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} = 1200 \, \text{g} \][/tex]
- Specific heat of the calorimeter, [tex]\( C_p = 3.55 \, \frac{\text{J}}{\text{g} \cdot \text{°C}} \)[/tex]
- Heat released by the combustion, [tex]\( q = 14.0 \, \text{kJ} \)[/tex]
- Convert the heat from kilojoules to joules:
[tex]\[ q = 14.0 \, \text{kJ} \times 1000 \, \frac{\text{J}}{\text{kJ}} = 14000 \, \text{J} \][/tex]

2. Use the heat transfer equation [tex]\( q = m C_p \Delta T \)[/tex] where [tex]\( \Delta T \)[/tex] is the change in temperature. Rearrange the equation to solve for [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = \frac{q}{m C_p} \][/tex]

3. Substitute the given values into the formula:
[tex]\[ \Delta T = \frac{14000 \, \text{J}}{1200 \, \text{g} \times 3.55 \, \frac{\text{J}}{\text{g} \cdot \text{°C}}} \][/tex]

4. Calculate the change in temperature:
[tex]\[ \Delta T = \frac{14000}{1200 \times 3.55} \approx \frac{14000}{4260} \approx 3.29^\circ C \][/tex]

5. Determine the final temperature of the calorimeter:
[tex]\[ T_{\text{final}} = T_{\text{initial}} + \Delta T \][/tex]
[tex]\[ T_{\text{final}} = 22.5^\circ C + 3.29^\circ C = 25.79^\circ C \][/tex]

Given the calculations, the final temperature of the calorimeter is approximately [tex]\( 25.8^\circ C \)[/tex].

So, the correct answer is:
[tex]\[ \boxed{25.8^\circ C} \][/tex]
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