100K,\] tem. Of surrounding \[{{T}_{0}}=0K\], initial temperature of body \[T=200\text{ }K\]]\[\frac{100}{dt}=\frac{\sigma 4\pi {{r}^{2}}}{\frac{4}{3}\pi {{r}^{3}}\rho CJ}({{200}^{4}}-{{0}^{4}})\]\[\RIGHTARROW dt=\frac{r\rho cJ}{48\sigma }\times {{10}^{-6}}s=\frac{r\rho c}{\sigma }.\frac{4.2}{48}\times {{10}^{-6}}\]\[=\frac{7}{80}\frac{r\rho c}{\sigma }\mu s\approx \frac{7}{72}\frac{r\rho c}{\sigma }\mu s[AsJ=4.2]\]

"> 100K,\] tem. Of surrounding \[{{T}_{0}}=0K\], initial temperature of body \[T=200\text{ }K\]]\[\frac{100}{dt}=\frac{\sigma 4\pi {{r}^{2}}}{\frac{4}{3}\pi {{r}^{3}}\rho CJ}({{200}^{4}}-{{0}^{4}})\]\[\RIGHTARROW dt=\frac{r\rho cJ}{48\sigma }\times {{10}^{-6}}s=\frac{r\rho c}{\sigma }.\frac{4.2}{48}\times {{10}^{-6}}\]\[=\frac{7}{80}\frac{r\rho c}{\sigma }\mu s\approx \frac{7}{72}\frac{r\rho c}{\sigma }\mu s[AsJ=4.2]\]

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A solid copper sphere (density \[\rho \] 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 \[\mu s\]) for the temperature of the sphere to drop to 100 K is

NEET Physics in NEET 1 year ago

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[b] \[\frac{dT}{dt}=\frac{\sigma A}{mcJ}({{T}^{4}}-{{T}_{0}}^{4})\][in the given problem, fall in temperature of body \[dT=(200-100)=100K,\] tem. Of surrounding \[{{T}_{0}}=0K\], initial temperature of body \[T=200\text{ }K\]]\[\frac{100}{dt}=\frac{\sigma 4\pi {{r}^{2}}}{\frac{4}{3}\pi {{r}^{3}}\rho CJ}({{200}^{4}}-{{0}^{4}})\]\[\RIGHTARROW dt=\frac{r\rho cJ}{48\sigma }\times {{10}^{-6}}s=\frac{r\rho c}{\sigma }.\frac{4.2}{48}\times {{10}^{-6}}\]\[=\frac{7}{80}\frac{r\rho c}{\sigma }\mu s\approx \frac{7}{72}\frac{r\rho c}{\sigma }\mu s[AsJ=4.2]\]

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