The specific heat of a substance at temperature t ^∘ C is s=a t^2+b t+c . The amount of heat req

step 1 Hello students in this question we have given the specific heat as equals to a t squared plus b

The specific heat of a substance at temperature t ^∘ C is...

The specific heat of a substance at temperature $t{ }^{\circ} \mathrm{C}$ is $s=a t^{2}+b t+c .$ The amount of heat required to raise the temperature of $m \mathrm{~g}$ of the substance from $0^{\circ} \mathrm{C}$ to $t_{0}^{\circ} \mathrm{C}$, is : (a) $\frac{m t_{0}^{2} a}{3}+\frac{b t_{0}^{2}}{2}+c t_{0}$ (b) $\frac{m t_{0}^{3} a}{3}+\frac{m b t_{0}^{2}}{2}+m c t_{0}$ (c) $\frac{m t_{0}^{3} a}{3}+\frac{m b t_{0}^{2}}{2}$ (d) none of these

The specific heat of a substance at temperature $t{ }^{\circ} \mathrm{C}$ is $s=a t^{2}+b t+c .$ The amount of heat required to raise the temperature of $m \mathrm{~g}$ of the substance from $0^{\circ} \mathrm{C}$ to $t_{0}^{\circ} \mathrm{C}$, is :
(a) $\frac{m t_{0}^{2} a}{3}+\frac{b t_{0}^{2}}{2}+c t_{0}$
(b) $\frac{m t_{0}^{3} a}{3}+\frac{m b t_{0}^{2}}{2}+m c t_{0}$
(c) $\frac{m t_{0}^{3} a}{3}+\frac{m b t_{0}^{2}}{2}$
(d) none of these

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Key Concepts

Specific Heat Capacity

Specific heat capacity is a property of a substance that indicates the amount of heat required to raise the temperature of a unit mass of the substance by one degree Celsius. It is a fundamental concept in thermodynamics and plays a critical role in understanding how substances absorb and store thermal energy.

Integration in Calculus

Integration is a mathematical technique used to calculate the accumulation of quantities, such as area under a curve or total change over an interval. In the context of variable specific heat, the integration process sums the incremental amounts of heat added over a temperature range, accounting for how the specific heat varies with temperature.

Heat Energy Calculation for Variable Specific Heat

When the specific heat of a substance is dependent on temperature, the total heat required to change the temperature is obtained by integrating the specific heat function over the temperature change. This method is essential in scenarios where the specific heat is not constant, ensuring an accurate calculation of the energy needed based on the changing thermal properties.

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