A) \[5\times {{10}^{4}}Dm\]
B) \[(33/4)\times {{10}^{4}}Dm\]
C) \[(65/4)\times {{10}^{4}}Dm\]
D) \[(5/4)\times {{10}^{4}}Dm\]
Correct Answer: C
Solution :
[c] : As \[\Delta Q=mc\Delta T\] \[\therefore \]\[Q=\int_{{}}^{{}}{\Delta Q}=\int\limits_{{{T}_{1}}}^{{{T}_{2}}}{mc\Delta T}\] Here,\[c=D{{T}^{3}},{{T}_{1}}=20K\]and\[{{T}_{2}}=30K\] \[\therefore \]\[Q=\int\limits_{20}^{30}{mD{{T}^{3}}dT=mD}\int\limits_{20}^{30}{{{T}^{3}}dT}=mD\left[ \frac{{{T}^{4}}}{4} \right]_{20}^{30}\] \[=\frac{mD}{4}[{{(30)}^{4}}-{{(20)}^{4}}]=\frac{mD}{4}\times {{10}^{4}}[81-16]\] \[=\left( \frac{65}{4} \right)\times {{10}^{4}}Dm\]
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