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Standard XII

Physics

1st Law of Thermodynamics

What is the d...

Question

What is the dimensional formula for thermal resistance?

[M^{- 1}

L^{-}

^{2}

T^{-}

^{1}

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[M L^{2}

T^{-}

^{2}

K^{-}

^{1}

]

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[

M L^{-}

^{3}

T^{2}

K^{- 1}

]

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[

M^{-}

^{1}

L^{-}

^{2}

T^{3}

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Solution

The correct option is D [ $M^{-}$ $^{1}$ $L^{-}$ $^{2}$ $T^{3}$ K]
We know,
$Thermal Resistance = \frac{Temperature difference}{Thermal current} = \frac{Δ T}{rate of flow of heat} ⟹ = \frac{Δ T}{\frac{Δ Q}{Δ t}} = \frac{[K]}{[M L^{2} T^{- 3}]} = [M^{- 1} L^{- 2} T^{3} K]$
is the dimensional formula for thermal resistance

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, dimensional formula of

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Q. Match the Column I with Column II

	Column I (Units)		Column II (Dimensional formulae)
(A)	Pa s	(p)	$[M^{0} L^{2} T^{- 2} K^{- 1}]$
(B)	N m K $^{- 1}$	(q)	$[M L T^{- 3} K^{- 1}]$
(C)	J kg $^{- 1}$ K $^{- 1}$	(r)	$[M L^{- 1} T^{- 1}]$
(D)	W m $^{- 1}$ K $^{- 1}$	(s)	$[M L^{2} T^{- 2} K^{- 1}]$

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

Q. Names of units of some physical quantities are given in List - I and their dimensional formulae are given in List - II. Match the correct pair of the lists.

List - I	List - II
a) Pa-s	e) $[L^{2} T^{- 2} K^{- 1}]$
b) ${N m K}^{- 1}$	f) ${M L T}^{- 3} K^{- 1}$
c) ${J k g}^{- 1} k^{- 1}$	g) ${M L}^{- 1} T^{- 1}$
d) ${W m}^{- 1} k^{- 1}$	h) $[{M L}^{2} T^{- 2} K^{- 1}]$

In a direct impact, loss in kinetic energy is given by
$Δ K = \frac{M_{1} M_{2}}{2 (M_{1} + M_{2})} . (V_{1} - V_{2})^{2} (1 - k^{2})$
with usual notations (except k). The quantity k will have dimensional formula:

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What is the dimensional formula for thermal resistance?

The correct option is D [M− 1 L− 2 T3K]We know,Thermal Resistance=Temperature differenceThermal current=ΔTrate of flow of heat⟹=ΔTΔQΔt=[K][ML2T−3]=[M−1L−2T3K]is the dimensional formula for thermal resistance