Answer:
dT(t)/dt = k[T5 - T(t)]
Explanation:
Since T(t) represents the temperature of the object and T5 represents the temperature of the surroundings, according to Newton's law of cooling, the rate at which an object's temperature changes is directly proportional to the difference in temperature between the object and the surrounding medium, that is dT(t)/dt ∝ T5 - T(t)
Introducing the constant of proportionality
dT(t)/dt = k[T5 - T(t)]
which is the desired differential equation
Answer:

Explanation:
The intensity of an electromagnetic wave can be expressed in terms of the magnetic field using the next relationship:
(1)
- c is the speed of light (3*10⁸ m/s)
- μ₀ is the permeability of free space (in vacuum ) (1.26*10⁻⁶ N/A²)
- B₀ is the magnetic field


Now, let's define the relationship between power (P) and average intensity (I).

- P is the power
- A is the area crossed
So we can calculate the power.

Finally, energy is the product of P times time, so:

I hope it helps you!
Answer:
Temperature, T = 1542.10 K
Explanation:
It is given that,
The black body radiation emitted from a furnace peaks at a wavelength of, 
We need to find the temperature inside the furnace. The relationship between the temperature and the wavelength is given by Wein's law i.e.

or

b = Wein's displacement constant



T = 1542.10 K
So, the temperature inside the furnace is 1542.10 K. Hence, this is the required solution.