10-2.Transmission of Heat
medium

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

A

$(3/16)H$

B

$(16/3)H$

C

$(9/27)H$

D

$(1/16)H$

Solution

(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}}}$

or $H' = \frac{{(16 + 4)(16 – 4)H}}{{(36 + 4)(36 – 4)}}$$ = \frac{3}{{16}}H$

Standard 11
Physics

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