Question

The specific heat of a solid at low temperature varies according to the relation $c=k{T}^3$ where $k$ is a constant and $T$ is temperature in kelvin. The heat required to raise the temperature of a mass $m$ of such a solid from $T=0K$ to $T=20K$ is:

• A. $2\times {10}^{4}mk$
• B. $4\times {10}^{4}mk$
• C. $8\times {10}^{4}mk$
• D. $16\times {10}^{4}mk$

Answer 1

Answer: (B)

$4\times {10}^{4}mk$

The heat required for increasing the temperature can be obtained by integrating the small Q. Thus, The correct answer is B

$Q=\int mc\Delta t;Q={\int }_0^{20}\left(mk{T}^3\right)=(mh{T}^4{)}_0^{20};Q=4\times {10}^{4}mk$