To determine the amount of heat required to warm 10 kg of carbon dioxide (CO2) gas from 70°C to 25°C, we can use the formula:
Q = m × c × ΔT
Where:
- Q = heat energy (in joules)
- m = mass of the substance (in kg)
- c = specific heat capacity (in J/kg°C)
- ΔT = change in temperature (in °C)
Given:
- m = 10 kg
- c = 0.84 J/g°C (which is equivalent to 840 J/kg°C)
- Initial temperature = 70°C
- Final temperature = 25°C
The change in temperature (ΔT) can be calculated as follows:
ΔT = Final temperature – Initial temperature = 25°C – 70°C = -45°C
Now, substituting the values into the formula:
Q = 10 kg × 840 J/kg°C × (-45°C)
Calculating this gives:
Q = 10 × 840 × -45 = -378000 J
This means that the CO2 gas actually releases 378,000 joules of heat in order to cool down from 70°C to 25°C. Hence, the required heat is negative, indicating that heat is being lost rather than gained.