The specific heat capacity of a substance is temperature dependent and is given by the formula $C=k T$, where $k$ is a constant of suitable dimensions in SI units, and $T$ is the absolute temperature. If the heat required to raise the temperature of $1 \mathrm{~kg}$ of the substance from…

Question

The specific heat capacity of a substance is temperature dependent and is given by the formula $C=k T$, where $k$ is a constant of suitable dimensions in SI units, and $T$ is the absolute temperature. If the heat required to raise the temperature of $1 \mathrm{~kg}$ of the substance from $-73^{\circ} \mathrm{C}$ to $27^{\circ} \mathrm{C}$ is $n k$, the value of $n$ is _____ [Given: $0 \mathrm{~K}=-273^{\circ} \mathrm{C}$.]

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{T}_{\mathrm{i}}=-73^{\circ} \mathrm{C}=200 \mathrm{~K} \ & \mathrm{~T}_{\mathrm{f}}=27^{\circ} \mathrm{C}=300 \mathrm{~K}\end{aligned}$ $\begin{aligned} & \mathrm{Q}=\int \mathrm{msdT} \ & =\int 1 \cdot \mathrm{kTdT} \ & =\int \mathrm{kTdT}=\mathrm{K} \int_{200}^{300} \mathrm{TdT} \ & =\frac{\mathrm{K}}{2}\left[\mathrm{~T}^2ight]_{200}^{300}=\frac{\mathrm{K}}{2}\left[300^2-200^2ight] \ & \mathrm{Q}=25000 \mathrm{~K}\end{aligned}$ Hence $n=25000$

The specific heat capacity of a substance is temperature dependent and is given by the formula $C=k T$,…

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