2. Questions Bank
  3. JEE Main & Advanced
  4. Physics
  5. Transmission of Heat

JEE Main & Advanced Physics Transmission of Heat Question Bank Critical Thinking

  • question_answer
    A solid copper sphere (density \[\rho \] and specific heat capacity c) of radius r at an initial temperature 200K is suspended inside a chamber whose walls are at almost 0K. The time required (in \[\mu \]s) for the temperature of the sphere to drop to 100 K is                                  [IIT-JEE 1991]

    A)            \[\frac{72}{7}\frac{r\rho c}{\sigma }\]                                   

    B)            \[\frac{7}{72}\frac{r\rho c}{\sigma }\]

    C)            \[\frac{27}{7}\frac{r\rho c}{\sigma }\]                                   

    D)            \[\frac{7}{27}\frac{r\rho c}{\sigma }\]

    Correct Answer: B

    Solution :

                       \[\frac{dT}{dt}=\frac{\sigma \,A}{mcJ}\,\,({{T}^{4}}-T_{0}^{4})\]  [In the given problem fall in temperature of body \[dT=(200-100)=100K\], temp. of surrounding T0 = 0K, Initial temperature of body \[T=200K].\] \[\frac{100}{dt}=\frac{\sigma 4\pi {{r}^{2}}}{\frac{4}{3}\pi {{r}^{3}}\rho \,c\,J}({{200}^{4}}-{{0}^{4}})\] Þ \[dt=\frac{r\rho \,c\,J}{48\sigma }\times {{10}^{-6}}s=\frac{r\rho \,c}{\sigma }.\frac{4.2}{48}\times {{10}^{-6}}\]          \[=\frac{7}{80}\frac{r\rho \,c}{\sigma }\mu \,s\tilde{}\frac{7}{72}\frac{r\rho \,c}{\sigma }\mu \,s\]       [As J = 4.2]


You need to login to perform this action.
You will be redirected in 3 sec spinner