The energy required to heat or cool a substance can be calculated using the following equation:
Q = mcΔT
where:
Q is the energy required, in Joules (J) m is the mass of the substance, in kilograms (kg) c is the specific heat capacity of the substance, in Joules per kilogram degrees Celsius (J/kg°C) ΔT is the change in temperature of the substance, in degrees Celsius (°C) In this case, we are comparing the energy required to heat the air from 15 to 16 degrees Celsius to the energy required to cool the air from 15 to 14 degrees Celsius. Let's assume that the mass of the air and its specific heat capacity are the same in both cases.
To calculate the energy required to heat the air, we can plug the values into the equation as follows:
Q = mcΔT = (m)(c)(16 - 15) = (m)(c)(1)
To calculate the energy required to cool the air, we can use the same equation:
Q = mcΔT = (m)(c)(15 - 14) = (m)(c)(1)
In both cases, the energy required (Q) is equal to the product of the mass of the air (m), its specific heat capacity (c), and the change in temperature (ΔT). Since the mass and specific heat capacity are the same in both cases, the energy required is also the same. However, the sign of the change in temperature is different: it is positive when heating the air and negative when cooling the air.
Since the energy required to heat or cool a substance is proportional to the change in temperature, it will take more energy to heat the substance by a given amount than it will take to cool it by the same amount. In this case, it will take more energy to heat the air from 15 to 16 degrees Celsius than it will take to cool it from 15 to 14 degrees Celsius.