The specific heat of a substance at temperatu | vedclass

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(B) The heat required to change the temperature of a substance by $dT$ is given by $dQ = m C dT$.Substituting the given expression for specific heat $

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$\frac{m T_o^3 \alpha}{3} + \frac{m \beta T_o^2}{2} + m \gamma T_o$

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(B) The heat required to change the temperature of a substance by $dT$ is given by $dQ = m C dT$.Substituting the given expression for specific heat $C = \alpha T^2 + \beta T + \gamma$,we get:$dQ = m (\alpha T^2 + \beta T + \gamma) dT$To find the total heat $Q$ required to raise the temperature from $0^{\circ}C$ to $T_o^{\circ}C$,we integrate the expression:$Q = \int_{0}^{T_o} m (\alpha T^2 + \beta T + \gamma) dT$$Q = m \left[ \frac{\alpha T^3}{3} + \frac{\beta T^2}{2} + \gamma T \right]_{0}^{T_o}$$Q = m \left( \frac{\alpha T_o^3}{3} + \frac{\beta T_o^2}{2} + \gamma T_o \right)$$Q = \frac{m \alpha T_o^3}{3} + \frac{m \beta T_o^2}{2} + m \gamma T_o$

The specific heat of a substance at temperature $T^{\circ}C$ is given by $C = \alpha T^2 + \beta T + \gamma$. The amount of heat required to raise the temperature of a mass $m \, g$ of the substance from $0^{\circ}C$ to $T_o^{\circ}C$ is .......

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