Advertisements
Advertisements
प्रश्न
Newton's law of cooling is a special case of
पर्याय
Wien's displacement law
Kirchhoff's law
Stefan's law
Planck's law
Advertisements
उत्तर
Stefan's law
From Stefan-Boltzman's law, the energy of the thermal radiation emitted per unit time by a blackbody of surface area A is given by, `u = σAT^4`
Where `σ` is Stefan's constant.
Suppose a body at temperature T is kept in a room at temperature T0.
According to Stefan's law, energy of the thermal radiation emitted by the body per unit time is `u = eσAT^4`
Here, e is the emissivity of the body.
The energy absorbed per unit time by the body is (due to the radiation emitted by the walls of the room
`Δu = eσAT_0^4`
Thus, the net loss of thermal energy per unit time is
`Δu = eσA ( T^4 - T_0^4 )`
Newton law of cooling is given by
`(dT)/(dt) = -bA( T - T_0 )`
This can be obtained from equation (i) by considering the temperature difference to be small and doing the binomial expansion.
APPEARS IN
संबंधित प्रश्न
A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of the surroundings is 20 °C.
On a cold winter night you are asked to sit on a chair. Would you like to choose a metal chair or a wooden chair? Both are kept in the same lawn and are at the same temperature.
An ordinary electric fan does not cool the air, still it gives comfort in summer. Explain
The temperature of the atmosphere at a high altitude is around 500°C. Yet an animal there would freeze to death and not boil. Explain.
A metal sphere cools from 80 °C to 60 °C in 6 min. How much time with it take to cool from 60 °C to 40 °C if the room temperature is 30 °C?
A bucket full of hot water cools from 85 °C to 80 °C in time T1, from 80 °C to 75 °C in time T2 and from 75 °C to 70 °C in time T3, then ______.
Rate of cooling of a body is 0.4 °C/min when excess temperature is 20 °C. The proportionality constant is ______.
A metal sphere cools from 66° C to 57° C in 10 minutes and to 44° C in the next 10 minutes. The ratio of fall of temperature of first 10 minutes to next ten minutes is ____________.
Newton's law of cooling leads to the expression:
A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken for a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is ______
A glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is correct?
- The rate of cooling is constant till milk attains the temperature of the surrounding.
- The temperature of milk falls off exponentially with time.
- While cooling, there is a flow of heat from milk to the surrounding as well as from surrounding to the milk but the net flow of heat is from milk to the surounding and that is why it cools.
- All three phenomenon, conduction, convection and radiation are responsible for the loss of heat from milk to the surroundings.
Is the bulb of a thermometer made of diathermic or adiabatic wall?
According to Newton's law of cooling, the rate of cooling of the body is proportional to (Δθ), where Δθ is the difference between the temperature of the body and the surroundings, and n is equal to ______.
According to Newton's law of cooling, how does the rate of cooling depend on temperature?
In \[\frac{dT}{dt}\] = C(T−T₀), what does the constant C represent?
What is the shape of the cooling curve T vs t?
A body cools from temperature \[(3\theta)^{\circ}C\] to \[(2\theta)^{\circ}C\] in 10 minute. Then it cools from \[(2\theta)^{\circ}C\] to \[(\theta_1)^{\circ}C\] in next 10 minutes. The room temperature is \[(\theta)^{\circ}C.\] Assuming that the newton's law of cooling is applicable the value of \[(\theta_1)^{\circ}C\] is ______.
The cooling curve of a hot body is a graph of temperature T versus time t. What is the correct description of this curve?
