Let's solve the problem step by step, considering all given variables and using the provided equation for heat transfer, [tex]\( q = m C \Delta T \)[/tex].
1. Given Information:
- Mass of the calorimeter, [tex]\( m = 1.00 \, \text{kg} \)[/tex]
- Specific heat capacity of the calorimeter, [tex]\( C = 1.50 \, \text{J/(g°C)} \)[/tex]
- Initial temperature, [tex]\( T_{i} = 21.0 \, \text{°C} \)[/tex]
- Final temperature, [tex]\( T_{f} = 41.0 \, \text{°C} \)[/tex]
2. Convert the mass to grams:
[tex]\[ m = 1.00 \, \text{kg} \times 1000 \, \text{g/kg} = 1000 \, \text{g} \][/tex]
3. Calculate the temperature change [tex]\( \Delta T \)[/tex]:
[tex]\[ \Delta T = T_{f} - T_{i} = 41.0 \, \text{°C} - 21.0 \, \text{°C} = 20.0 \, \text{°C} \][/tex]
4. Calculate the heat released [tex]\( q \)[/tex]:
[tex]\[ q = m C \Delta T \][/tex]
[tex]\[ q = 1000 \, \text{g} \times 1.50 \, \text{J/(g°C)} \times 20.0 \, \text{°C} \][/tex]
[tex]\[ q = 1000 \times 1.50 \times 20.0 \, \text{J} \][/tex]
[tex]\[ q = 30000.0 \, \text{J} \][/tex]
5. Convert the heat released to kilojoules (kJ):
[tex]\[ q = \frac{30000.0 \, \text{J}}{1000} = 30.0 \, \text{kJ} \][/tex]
Thus, the amount of heat released during the combustion of the octane sample is [tex]\( \boxed{30.0 \, \text{kJ}} \)[/tex].
