A sphere at temperature $600\,K$ is placed in an environment of temperature is $200\,K$ . Its cooling rate is $H$ . If its temperature reduced to $400\,K$ then cooling rate in same environment will become
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(a) Rate of cooling $ \propto ({T^4} - T_0^4)$
.==> $\frac{H}{{H'}} = \frac{{(T_1^4 - T_0^4)}}{{(T_2^4 - T_0^4)}} = $$\frac{{{{400}^4} - {{200}^4}}}{{{{600}^4} - {{200}^4}}}$
.==> $\frac{H}{{H'}} = \frac{{(T_1^4 - T_0^4)}}{{(T_2^4 - T_0^4)}} = $$\frac{{{{400}^4} - {{200}^4}}}{{{{600}^4} - {{200}^4}}}$
or $H' = \frac{{(16 + 4)(16 - 4)H}}{{(36 + 4)(36 - 4)}}$$ = \frac{3}{{16}}H$
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