Question

How to find the dimension of conductance

Answer 1

heya.....,,,,,, .....

Answer 2

Derivation of Thermal Conductivity Expression

Now we will derive the Thermal Conductivity expression. Suppose heat energy Q is flowing through a rod of length L in time t.

The temperature values of the two ends of the rod are T1 and T2. (Say, T1>T2)

Then the Rate of Flow of Heat i.e. Q/t, through the rod in the steady state is

Proportional to the cross-sectional area A of the rod and

Proportional to the temperature difference (T1-T2) between the two ends of the rod and

Inversely proportional to the length or thickness (L) of the rod.

            Q/t ∝  [A (T1-T2)]/L

=>     Q/t = [k A (T1-T2)] / L,

where k is a constant called the thermal conductivity of the material of the rod.
====> k = [Q L] / [A (T1-T2) t ]    …………………… (1)

From equation 1, we can clearly see that k = (Q/t).L.A-1(T1-T2)-1
From this equation we will gradually derive the dimension.Let’s read on to get it.
And we know, Dimension of Q/t is equal to the dimension of Work/time or  i.e. Power.

Dimension of L.A-1 is equal to that of L-1 actually. (as A = L2)

Temperature difference (T1-T2) can be designated with Theta (θ)

So Thermal Conductivity= (Unit of Power) (unit of length)-1(unit of temperature)-1 _____________ (2)

Breaking these down for simplicity,

Power = Work/time = (force X displacement) / time

= (mass X acceleration X Displacement)time-1

So, Power = M (LT-2) L T-1= (ML2)(T-3)_________(3)

Putting the dimension of Work in equation 2,

Dimension of Thermal Conductivity (k) = (ML2)(T-3) L-1 θ-1 =  M1 L1  T -3  θ -1  



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