The question asks how much air can be cooled by 1.0°C if the energy is transferred from the air to water, increasing the temperature of 1.0 kg of water by 1.0°C. To calculate this, we need to consider the specific heat capacities of air and water.
1. Calculate the energy transferred from air to water using the specific heat capacities:
- Specific heat capacity of air = 1000 J/kg°C
- Mass of water = 1.0 kg
- Change in temperature of water = 1.0°C
2. Calculate the energy transferred from air to water:
Energy transferred = mass of water × specific heat capacity of water × change in temperature
Energy transferred = 1.0 kg × 4186 J/kg°C × 1.0°C
3. Now, convert this energy into the amount of air that can be cooled by 1.0°C:
- Density of air = 1.29 kg/m³
4. Calculate the volume of air that can be cooled by 1.0°C:
Volume of air = Energy transferred / (specific heat capacity of air × density of air)
Volume of air = (1.0 kg × 4186 J/kg°C × 1.0°C) / (1000 J/kg°C × 1.29 kg/m³)
5. After performing the calculations, the result is 71 liters of air that can be cooled by 1.0°C when the energy is transferred from the air to water.
