Question

The specific heat of many solids at low temperatures varies with absolute temperature T according to the graph as shown. Then heat energy required to raise the temperature of a unit mass of such a solid from T $=$ 0 to T$=$ 30K is

• A. $300\sqrt{3}$ J
• B. $900\sqrt{3}$ J
• C. $450\sqrt{3}$ J
• D. $150\sqrt{3}$ J

Answer 1

The correct option is C $450\sqrt{3}$ J

$Q={\int }_0^{T}SdT$
$={\int }_0^T\sqrt{3}T\cdot dT=\frac{\sqrt{3}}{2}[T^2{]}_0^{30}=\frac{\sqrt{3}}{2}\times 900=450\sqrt{3}$ J.