2. Questions Bank
  3. NEET
  4. Physics
  5. Thermometry, Calorimetry & Thermal Expansion

NEET Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Mock Test - Thermal Properties of Matter

  • question_answer
    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

    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 :

    [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 \[T=200\text{ }K\]] \[\frac{100}{dt}=\frac{\sigma 4\pi {{r}^{2}}}{\frac{4}{3}\pi {{r}^{3}}\rho cJ}({{200}^{4}}-{{0}^{4}})\] \[\Rightarrow dt=\frac{r\rho cJ}{48\sigma }\times {{10}^{-6}}s=\frac{r\rho c}{\sigma }.\frac{4.2}{48}\times {{10}^{-6}}\] \[=\frac{7}{80}\frac{r\rho c}{\sigma }\mu s\approx \frac{7}{72}\frac{r\rho c}{\sigma }\mu s[AsJ=4.2]\]


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