Question

Match the following

a) Thermal resistance	e) $M{T}^{-3}{K}^{-4}$
b) Stefan's constant	f) $ML{T}^{-3}{K}^{-1}$
c) Wein's constant	g) $M^{-1}{L}^{-2}{T}^{3}K$
d) coefficient of thermal conductivity	h) $M^{o}LK$

• A. a - e, b - g, c - h, d - f
• B. a - f, b - h, c - e, d - g
• C. a - g, b - e, c - h, d - f
• D. a - g, b - h, c - e, d - f

Answer 1

Answer: (C)

a - g, b - e, c - h, d - f

$\frac{△Q}{△t}=\frac{△\theta }{R}$

Thermal resistance: $R=\frac{△Q△t}{△Q}=\frac{KT}{M{L}^2{T}^{-2}}$

dimension of thermal resistance $\Rightarrow \left[M^{-1}{L}^{-2}{T}^{3}K\right]$

Stefan's constant: $\frac{△Q}{△t}=e\sigma A{T}^4\Rightarrow \sigma =\frac{△Q}{△teA{T}^{-4}}\Rightarrow \frac{M{L}^2{T}^{-2}}{T{L}^2{K}^4}$

Dimension of stefan constant: $\left[M{T}^{-3}{K}^{-4}\right]$

Wein's constant: ${\lambda }_{max}=\frac{b}{T}\Rightarrow b={\lambda }_{max}T$

Dimension of wein constant: $\left[M^{0}LK\right]$

Coefficient of thermal of conductivity:

$\frac{△Q}{△t}=\frac{△\theta }{\frac{l}{KA}}=\frac{KA△\theta }{l}\Rightarrow K=\frac{l△Q}{△tA△\theta }$

Dimension of $K=\left[ML{T}^{-3}{K}^{-1}\right]$