The specific heat of a metal at low temperatu | vedclass

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Question

(B) The heat energy $dQ$ required to raise the temperature of a unit mass $(m = 1)$ by a small amount $dT$ is given by $dQ = m \cdot S \cdot dT$.Subst

Vedclass · Accepted Answer

$\frac{15 \ a}{4}$

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(B) The heat energy $dQ$ required to raise the temperature of a unit mass $(m = 1)$ by a small amount $dT$ is given by $dQ = m \cdot S \cdot dT$.Substituting $S = aT^3$ and $m = 1$,we get $dQ = aT^3 \ dT$.To find the total heat energy $Q$ required to raise the temperature from $T_1 = 1 \ K$ to $T_2 = 2 \ K$,we integrate the expression:$Q = \int_{1}^{2} aT^3 \ dT$$Q = a \left[ \frac{T^4}{4} \right]_{1}^{2}$$Q = \frac{a}{4} (2^4 - 1^4)$$Q = \frac{a}{4} (16 - 1)$$Q = \frac{15 \ a}{4}$

The specific heat of a metal at low temperatures varies according to $S = aT^3$,where $a$ is a constant and $T$ is the absolute temperature. The heat energy needed to raise unit mass of the metal from $T = 1 \ K$ to $T = 2 \ K$ is:

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