Questions
A solid copper sphere (density and specific heat capacity c) of radius r at an initial temperature 200 K is suspended inside a chamber whose walls are at almost 0 K. The time required (in s) for the temperature of the sphere to drop to 100 K is
detailed solution
Correct option is B
43πr3×ρCdTdt=σ4πr2T4⇒r3×ρCdTdt=σT4⇒rρC3σT4dT=dt⇒rρC3σ∫100200 dTT4=∫0t dt⇒rρC3σ∫100200 dTT4=∫0t dt⇒rρC9σ×1061−18=t∴t=7rρC72σ×106Similar Questions
A solid copper cube of edges 1 cm is suspended in an evacuated enclosure. Its temperature is found to fall from 100oC to 99oc in 100 s. Another solid copper cube of edges 2 cm, with similar surface nature, is suspended in a similar manner. The time required for this cube to cool from 100oC to 99oC will be approximately
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