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The specific heat \( c \) of a solid at low temperature shows temperature dependence according to the relation \( c=D T^{3} \)
\( \mathrm{P} \) where \( D \) is a constant and \( T \) is the temperature in kelvin. A piece of this solid of mass \( m \mathrm{~kg} \) is taken and its temperature
W is raised from \( 20 \mathrm{~K} \) to \( 30 \mathrm{~K} \). The amount of the heat required in the process in energy units is
[WB-JEE 2013]
(a) \( 5 \times 10^{4} \mathrm{Dm} \)
(b) \( (33 / 4) \times 10^{4} \mathrm{Dm} \)
(c) \( (65 / 4) \times 10^{4} \mathrm{Dm} \)
(d) \( (5 / 4) \times 10^{4} \mathrm{Dm} \)
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