Question

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

• A. $3a$
• B. $\frac{15a}{4}$
• C. $\frac{2a}{3}$
• D. $\frac{12a}{5}$

Answer 1

The correct option is B $\frac{15a}{4}$

At a temperature $T$
$dQ=SdT=a{T}^{3}dT$
$Q=a\underset{1}{\overset{2}{\int }}{T}^{3}dT=\frac{a[T^4{]}_1^2}{4}=\frac{15a}{4}$