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

Question

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

TestHub · Accepted Answer

​ ℓ = ℓ 0 ​ ( 1 + a Δ T ) ​ ⇒ ℓ − ℓ 0 ​ = ℓ 0 ​ a Δ T ​ ⇒ ℓ = ℓ 0 ​ a Δ T … ( i ) ​ Q = ms Δ T = ℓ 0 ​ α mc ⋅ ℓ ​ = ℓ 0 ​ α ( A ℓ 0 ​ d ) c ℓ ​ = α dAc ℓ ​

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