Question

State: (a) Wein’s displacement law, and (b) first law of thermodynamics.

Answer 1

Wein’s law deals with a black body's temperature (an ideal material that emits and absorbs all wavelengths of light) and the wavelength at which most light is emitted. It is also a known fact that energy can neither be created nor be destroyed.

Complete answer:
In the question, we are talking about the Wein’s displacement law and the first law of thermodynamics which is very important when we are dealing with black body radiation or thermodynamics. Let us explain the two laws below:

(a) Wein’s displacement law:
The displacement law of Wien states that for different temperatures, the black-body radiation curve will peak at different wavelengths that are inversely proportional to the temperature. The change of that peak is a direct consequence of the law of Planck radiation, which defines the black-body radiation spectral brightness as a function of wavelength at any specific temperature.
Formally, Wien's displacement law states that per unit wavelength, the spectral radiance of black-body radiation peaks at the wavelength ${\lambda _{{\text{peak}}}}$ is given as:
${\lambda _{{\text{peak}}}} = \dfrac{b}{T}$
Where,
$b$ indicates the proportionality constant specially called Wien’s displacement constant.
$T$ indicates the absolute temperature.

(b) First law of thermodynamics:
The first law of thermodynamics is a variant of the law of energy conservation, modified for thermodynamic processes, distinguishing between two forms of energy transfer, such as heat and thermodynamic work, and comparing them to a function called internal energy of the state of the body. The energy conservation law states that the total energy of an independent system is constant; energy can be converted from one form to another, but it can neither be generated nor destroyed. For a thermodynamic process without matter exchange, the first law is also proposed as:
$\Delta U = Q - W$
Where,
$\Delta U$ indicates the change in the internal energy of a closed system.
$Q$ indicates the amount of energy supplied to the system as heat.
$W$ indicates the amount of thermodynamic work done by the system on the surroundings.

Note: It is important to note that the law of displacement in Wien is useful in determining the temperatures of hot radiant objects such as stars, and indeed in determining the temperature of any radiant object whose temperature is much higher than that of its environment.