question_answer

Two identical beakers A and B contain equal volumes of two different liquids at \[60{}^\circ C\] each and left to cool down. Liquid in A has density of \[8\times {{10}^{2}}\,\,\text{kg/}{{\text{m}}^{3}}\]and specific heat of \[2000\,J\,k{{g}^{-\,1}}{{K}^{-\,1}}\]while liquid in B has density of \[{{10}^{3}}\,kg\,\,{{m}^{-\,3}}\]and specific heat of \[4000\,J\,k{{g}^{-1}}{{K}^{-1}}.\] Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

A)

B)

C)

D)

Correct Answer: C

Solution :

\[-\frac{dT}{dt}=\frac{e\sigma A}{ms}4T_{0}^{3}(T-{{T}_{0}})\propto \frac{1}{pS}\] For \[A\,\rho s=800\times 2000=16\times {{10}^{5}}\] \[B\rho s={{10}^{3}}\times 4000=40\times {{10}^{5}}\] \[{{(\rho s)}_{B}}>{{(\rho s)}_{A}}\] \[\Rightarrow \] \[{{\left( -\frac{dT}{dt} \right)}_{B}}<{{\left( -\frac{dT}{dt} \right)}_{A}}.\]