I鈥檓 sure you have been told or have even been the one to tell someone to 鈥渃lose the door鈥� because they were 鈥渓etting the cold in鈥�. While efforts to keep the house warm are noble, the advice is not supported by science. Cold cannot be let in because it doesn鈥檛 exist! Well, sort of.
Cold is simply the absence of heat, so technically speaking, feeling cold is just because you are less hot. The same applies to opening the door, the cold isn鈥檛 actually coming in, it is the warm air in front of the door that has exited allowing it to be replaced with the 鈥渃older鈥� air (or rather the one with less heat). Warmer air constantly seeks equilibrium and will attempt to move towards the colder air to adjust it to the same temperature. However, its success in doing so will depend on the amount of air present at each. Think of mixing water at 100 degrees Celsius with water at 20 degrees Celsius. The water with the higher temperature will try to bring the 鈥渃older鈥� water to 100 degrees. To do this, the hot water needs to transfer energy to the colder water, but the amount of energy available for transfer depends on the amount of hot water present. If the hot water is in abundance, it will be able to transfer more energy without significantly decreasing its temperature. However, if there is more cold water, then the hot water will have much less impact on its temperature.聽This process is explained by the heat transfer equation:
This equation relates the heat energy (Q) to the mass of the substance (m) and the temperature change that it goes through. The final term in the equation (c) is the specific heat capacity of the substance. The specific heat capacity is the amount of energy required to increase the temperature of one gram of a substance by 1 degree Celsius. For water, this value is 4.184 J/g掳C, which is the highest value of any substance. This is also a reason why water is extremely important biologically.
Now, going back to our air situation. We have our inside air (around 23掳C ) and the outside air (let鈥檚 say it is around 1掳C). When the door opens, the hot air escapes and tries to raise the temperature of the outside air, to no avail. This is because the amount of hot air is insignificant when compared to how much "cold"聽air is outside. It will not be able to increase the temperature, and it will eventually reach the same temperature of the outside air. If the door remains open, the warmer air inside the room will keep moving towards the door leaving cooler air. When we close the door, initially the room feels noticeably less warm, yet after some time, the warmer air from the rest of the house will have had enough time to transfer its heat energy in an attempt to raise the temperature of the air that was cooled by being near the door. In this case, the warmer air is in abundance and will be successful in raising the temperature of the room.
Instead of considering these as separate energy transfers, we can simply modify our heat transfer equation slightly. Since the energy evolved in the transfer is constant between both the hot and "cold" species, we can state that the energy lost by the hot air will be equal to the energy gained by the cold air. This is the basis of the 1st law of thermodynamics where energy cannot be created or destroyed, only transferred. Thus, if the hot species is losing energy, the "cold" one must be absorbing it.
In thermodynamics, the branch of physical science that studies heat and other forms of energy, the signs in equations inform us of the movement of the energy. If there is a negative sign, the energy is exiting the system (released), which is why there is a negative sign attributed to the energy of the hot species. A very common application of this equation is to find the equilibrium temperature, that is the temperature that the mixture of the hot and cold species will come to after they have been allowed to complete their transfer. We can therefore expand the equation above with a simple substitution.
Additionally, the change in temperature (鈭員) is defined as the final temperature of the mixture (Tf), minus the initial temperature of each individual substance (Ti). In the case of a heat transfer, both species involved will come to the same final temperature, the equilibrium temperature. This makes sense because it would be weird to have differing temperatures in a thoroughly mixed uniform mixture. In typical room conditions, the specific heat capacity of air is around 1.012 J/g掳C, and yes in actual thermodynamics we tend to use heat capacity (Cp and Cv) rather than specific heat capacity (C). Heat capacity differs if the measurement was taken at constant pressure or constant volume, making our lives much more complicated. Lucky for you, my goal isn鈥檛 to frighten you, so I think we鈥檙e fine with sticking to our nice and easy specific heat capacity (C) for this explanation.
Maybe you are not convinced that cold doesn鈥檛 truly exist, and I don鈥檛 blame you. I don鈥檛 step out onto the streets of Montreal at -20掳C and say, 鈥淥h it is less warm today鈥�. It is fine to qualify things as cold, but similarly to qualities like darkness and silence, they only exist due to the absence of something else.
鈥淏ut why does my hand feel cold after holding an ice cube?鈥� I鈥檓 going to be annoying but technically speaking your hand just feels less hot. A heat transfer took place right in the palm of your hand! Sure, it was a pretty tame one, but it is still pretty cool to consider. Your hand only feels 鈥渃old鈥� because when touching the ice聽it will lose energy to try to bring the ice up to the original temperature of your hand but will fail to do so quickly. This is because ice has a specific heat capacity of 2.03 J/g掳C which is still considerably high. The surface area of your hand is not that large in comparison to the ice cube so it will lose energy before it has a chance to completely melt the ice. After a while, the ice turns into water and your hand will probably feel 鈥渃old鈥� for quite some time, that is until your circulatory system will be able to pump some warmer blood back into the area (yet another heat transfer).
So now we have looked at some pretty useful chemistry. Whenever there is a difference in temperature between two substances that will interact, there will be a heat transfer until an equilibrium temperature is reached. The efficiency of the heat transfer and the equilibrium temperature depend on the mass of the components, their specific heat capacities and their initial temperatures.
Now remember, with winter fast approaching, keep your door closed, not because you will let the cold in, but because you will let the heat out.
Angelina Lapalme is a BSc student majoring in Bio-Organic Chemistry at 黑料不打烊 University.聽
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