Last time when I made a coffee, suddenly a question from 12th math flashed through my mind. It was a question that asked me to find the temperature of coffee after certain minutes. It seemed so funny to know the temperature of coffee.Why should I? But then I managed to memorise the formula and get marks(As I am supposed to ) Now ,being an engineer ,I was very much satiated to know the science behind and so, I did.
I found that this piece of sum depends on Newton's law of cooling in which the rate of heat loss of a substance is directly proportional to the ambient temperature and instantaneous temperature difference between substance and surrounding (This is why your coffee gets chilled faster in winters than as usual). Directly proportional doesn't mean that if ambient temperature is increased by two not necessarily increase heat loss by the same factor two but with some multiplicative factor usually called as heat loss co-efficient. This constant of proportionality varies usually for each and every substance. The heat loss is high when the temperature difference between substance and ambience is high and low when there is negligible difference in temperature. But this law is limited to temperature change in surroundings
Newton’s law of cooling is given by,
dT/dt = k(Tt – Ts)
Never try to remember those equations, just know the science behind. This simple piece of math gives us the application of calculus in real time. This also help us to approximate the time of death in postmortem reports , to design heat ex-changers in thermal power plants and a lot more.
I found that this piece of sum depends on Newton's law of cooling in which the rate of heat loss of a substance is directly proportional to the ambient temperature and instantaneous temperature difference between substance and surrounding (This is why your coffee gets chilled faster in winters than as usual). Directly proportional doesn't mean that if ambient temperature is increased by two not necessarily increase heat loss by the same factor two but with some multiplicative factor usually called as heat loss co-efficient. This constant of proportionality varies usually for each and every substance. The heat loss is high when the temperature difference between substance and ambience is high and low when there is negligible difference in temperature. But this law is limited to temperature change in surroundings
Newton’s law of cooling is given by,
dT/dt = k(Tt – Ts)
- Tt = temperature at time t and
- Ts = temperature of the surrounding,
- k = Positive constant that depends on the area and nature of the surface of the body under consideration.
- dT/dt = rate of heat loss
Never try to remember those equations, just know the science behind. This simple piece of math gives us the application of calculus in real time. This also help us to approximate the time of death in postmortem reports , to design heat ex-changers in thermal power plants and a lot more.
Hope you guys, liked the reading.
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