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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Introduction to Physics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Introduction to Physics

Find the dimensions of the specific heat capacity c . An equation...

Find the dimensions of the specific heat capacity

c

. An equation involving this quantity is

Q = mc(T_2 - T_1)

.

Options

A $L^2 T^{-2} K^{-1}$
B $L^2 T^{-2}$
C $M L T^{-2} K^{-1}$
D $ML^2 T^{-2} K^{-1}$

Correct answer

A. $L^2 T^{-2} K^{-1}$

Step-by-step solution

The given equation is

Q = mc(T_2 - T_1)

Rearranging for specific heat capacity

c

:

c = \dfrac{Q}{m(T_2 - T_1)}

The dimensional formula for heat energy

Q

is

[M L^2 T^{-2}]

The dimensional formula for mass

m

is

[M]

The dimensional formula for temperature difference

(T_2 - T_1)

is

[K]

Substituting these dimensions:

[c] = \dfrac{[M L^2 T^{-2}]}{[M][K]}

[c] = [L^2 T^{-2} K^{-1}]

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