Question

The dimension formula of thermal conductivity K given relation , Q = K

please help me ❤​

Answer 1

Solution,

We need to find the dimension formula of thermal conductivity K. It is called the coefficient of thermal conductivity. It is given by the formula as follows :

$K=\dfrac{Q\Delta x}{A\Delta T t}$

Here,

Q is heat

$\Delta x$ is length

A is area of cross section

$\Delta T$ is temperature

t is time

So,

Taking the dimensional formulas of all the quantities. So,

$K=\dfrac{[ML^2T^{-2}][L]}{[L^2][K][T]}\\\\K=[MLT^{-3}K^{-1}]$

So, the dimensional formula of K is $[MLT^{-3}K^{-1}]$.

Answer 2

Given that,

The relation is

$Q=\dfrac{kA\Delta T\times t}{\Delta x}$

We need to calculate the dimension formula of thermal conductivity

Using given relation

$Q=\dfrac{kA\Delta Tt}{\Delta x}$

$k=\dfrac{Q\Delta x}{A\Delta Tt}$

Where, Q = Heat

k =  thermal conductivity

t = time

A = area

T = temperature

x = length    

Put the dimension form in the relation

$k=\dfrac{ML^{2}T^{-2}L}{L^2KT}$

$k=MLT^{-3}K^{-1}$

Hence, The dimension formula of thermal conductivity is $MLT^{-3}K^{-1}$