What are Peltier and Thomson effects? Define their coefficients.

Hint: We can use the Peltier effect in those refrigerators which are compact and have no circulating fluid or moving parts. While the Thomson effect is the only one which can be measured for an individual material. So, we have to remember the principle Peltier effect of those refrigerators which are compact and have no circulating fluid or moving parts. We have to recall that principle which gives that coefficient which can be measured for an individual material.

Complete step by step answer:
Peltier effect: According to the Peltier effect, when an electric current is passed through a thermocouple circuit then at one junction the heat is evolved and at another junction the heat is absorbed. So, the Peltier effect states that in the electrified Junction of two conductors, the heating or cooling is present at the junction of the thermocouple circuit.
So, if the junction of a conductor is electrified then at the junction, the heat may be generated or removed.
Let \[A\] and \[B\] are two conductors then the heat generated at the junction per unit time is given as
\[\mathop Q\limits^ \bullet = \left( {{\Pi _A} - {\Pi _B}} \right)I\]
where ${\Pi _A}$ and ${\Pi _B}$ are the Peltier coefficients of the conductors \[A\]and \[B\], and $I$ is the electric current which is flowing in the junction of the conductors. Peltier coefficient represents carried heat per unit charge.

Thomson effect: According to Thomson effect, the Seebeck coefficient is not constant and a spatial gradient in temperature in different materials. So, a special gradient in temperature results in a gradient in the Seebeck coefficient. if a current is driven through this gradient then a continuous version of the Peltier effect will take place. This is predicted by Thomson and known as Thomson effect.
Let the current density \[J\] is passed through a conductor then the Thomson effect gives the heat production rate per unit volume
$\mathop q\limits^ \bullet = - {\rm K}J \bullet \nabla T$
Where $\nabla T$ is the temperature gradient and ${\rm K}$ is the Thomson coefficient which is related to Seebeck coefficient which is ${\rm K} = T\dfrac{{dS}}{{dT}}$.

Note:
In this question, we have to keep in mind that the Thomson effect is related with the gradient of the Seebeck coefficient. We have to keep in mind that the Peltier effect gives that at the electrified junction the heat will be generated or removed.