A) \[{{H}_{2}}=2{{H}_{1}}\]
B) \[{{H}_{2}}=\frac{{{H}_{1}}}{2}\]
C) \[{{H}_{2}}=\frac{{{H}_{1}}}{4}\]
D) \[{{H}_{2}}=4{{H}_{1}}\]
Correct Answer: A
Solution :
Key idea: Rate of heat flow is the ratio of heat transferred to the time interval. Rate of heat flow \[H=\frac{Q}{t}=\frac{KA({{\theta }_{1}}-{{\theta }_{2}})}{l}\] or \[H\propto \frac{A}{l}\] Since, dimensions of area \[(A)=[{{L}^{2}}]\] Dimensions of length (l) = [L] \[\therefore \] \[H\propto l\] or \[\frac{{{H}_{2}}}{{{H}_{1}}}=\frac{{{l}_{2}}}{{{l}_{1}}}=\frac{2{{l}_{1}}}{{{l}_{1}}}\] \[(\because {{l}_{2}}=2{{l}_{1}})\] or \[{{H}_{2}}=2{{H}_{1}}\]
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