Physics · Thermal Properties Of Matter · NEET
It states that the rate of loss of heat (or rate of fall of temperature) of a body is directly proportional to the excess of its temperature over the surroundings, provided this excess is small. As a formula: -dT/dt = k (T - T_surr), where k is a positive constant depending on the body's surface area, nature, and surroundings.
Because the rate of cooling depends on the temperature gap. When the body is very hot, the gap (T - T_surr) is large, so it cools fast (steep curve). As the body cools, the gap shrinks, so the rate slows down. The temperature approaches the surrounding temperature but never quite reaches it, giving an exponential decay curve that flattens.
No. Stefan-Boltzmann law (E proportional to T^4) is the exact law for radiation over any temperature range. Newton's law of cooling is an approximation of it that holds only for SMALL temperature differences between the body and its surroundings. For small gaps, the T^4 law reduces to a simple linear form, which is Newton's law.
You cannot use it when the temperature difference between the body and surroundings is large. The law is only a valid approximation for small excess temperatures. For large differences you must use the full Stefan-Boltzmann radiation law.
For a body cooling from T1 to T2 over a time t, we write (T1 - T2)/t = k[(T1 + T2)/2 - T_surr]. Here (T1+T2)/2 is the average temperature of the body during that interval, used because we approximate the rate over the whole interval. This linear form is the fast way to solve most NEET cooling problems.
A body cools from a temperature 3T to 2T in 10 minutes. The surroundings are at temperature T. Assuming Newton's law of cooling holds, the temperature of the body at the end of the next 10 minutes will be:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The rate of cooling equals a constant times the temperature difference: -dT/dt = k(T - T_surr). In interval form for solving problems: (T1 - T2)/t = k[(T1 + T2)/2 - T_surr].
A temperature-versus-time graph is an exponential decay curve. It starts steep (fast cooling when the gap is large) and gradually flattens, approaching the surrounding temperature but never crossing it.
The temperature difference between the body and surroundings must be small, the surroundings must stay at constant temperature, and heat loss must be mainly by radiation and convection under steady conditions.
No. The constant k depends on the surface area, the nature of the surface (emissivity), the mass and specific heat of the body, and the surroundings. A body with larger surface area cools faster.
Stefan's law gives heat loss proportional to (T^4 - T_surr^4). For a small excess temperature, this expression can be approximated to a form proportional to (T - T_surr), which is exactly Newton's law of cooling.
