The density of a uniform rod with cross - section A is d, its specific heat capacity is c and the coefficient of its linear expansion is α. Calculate the amount of heat that should be added in order to increase the length of the rod by ℓ.

Engineering

Physics

SI Units

Thermal Expansion

Calorimetry New

Question

The density of a uniform rod with cross - section A is d, its specific heat capacity is c and the coefficient of its linear expansion is α. Calculate the amount of heat that should be added in order to increase the length of the rod by ℓ.

$\frac{dAc l}{α}$

$\frac{dc l}{Aα}$

$\frac{αAc l}{d}$

$\frac{c l αd}{A}$

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Let length of rod = L
and heat supplied = ΔQ
∴ ΔQ = McΔT
also ℓ = LαΔT ; M = dLA

$∴ ΔQ = Mc \frac{l}{αL} = \frac{dAc l}{α}$ .