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 1kg of the substance from \(-73^{\circ} \mathrm{C}\) to \(27{ }^{\circ} \mathrm{C}\) is nk, the value of n is ___.

\( [Given: \left.0 \mathrm{~K}=-273^{\circ} \mathrm{C}.\right]\)

Answer 1

Correct answer is 25000

\(C=\frac{d Q / m}{d T}\)

\(\Rightarrow d Q=m \cdot C \cdot d T\)

\(=1 \cdot k T d T\)

\(Q=\int_{200}^{300} k T d T=\frac{k}{2}\left[300^{2}-200^{2}\right]\)

\(=\frac{10^{4}}{2} \cdot k \cdot 5\)

\(=25000 k\)

\(\Rightarrow n=25000\)