The specific heat C of a solid at low tempera | vedclass

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Question

(C) The amount of heat $Q$ required to raise the temperature of a substance is given by $Q = \int m C \ dT$.Given the specific heat $C = D T^{3}$.Subs

Vedclass · Accepted Answer

$(65 / 4) 	imes 10^{4} D m$

Vedclass · Answer

(C) The amount of heat $Q$ required to raise the temperature of a substance is given by $Q = \int m C \ dT$.Given the specific heat $C = D T^{3}$.Substituting this into the integral, we get $Q = \int_{20}^{30} m (D T^{3}) \ dT$.Taking the constants $m$ and $D$ outside the integral: $Q = m D \int_{20}^{30} T^{3} \ dT$.Evaluating the integral: $Q = m D \left[ \frac{T^{4}}{4} ight]_{20}^{30}$.$Q = \frac{m D}{4} [ (30)^{4} - (20)^{4} ]$.$Q = \frac{m D}{4} [ 810000 - 160000 ]$.$Q = \frac{m D}{4} [ 650000 ]$.$Q = \frac{650000}{4} m D = \frac{65}{4} 	imes 10^{4} m D$.

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