Question 76 of 126

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 $8\times {10}^{2}kg{m}^{-3}$ and specific heat of $2000Jk{g}^{-1}{K}^{-1}$ while the liquid in $B$ has density ${10}^{3}kg{m}^{-3}$ and specific heat of $4000Jk{g}^{-1}{K}^{-1}$. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

ABCD

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Answer: (B)

From Newton's law of cooling,
Rate of cooling: $\left(-\dfrac{dT}{dt}\right)=\dfrac{4\sigma eA{T}_{0}^{3}\left(T-{T}_{0}\right)}{ms}$$\propto \dfrac{1}{ms}$
$∴{\rho }_{A}\lt {\rho }_{B}$
${m}_{A}\lt {m}_{B}$
And ${s}_{A}\lt {s}_{B}$
${m}_{A}{s}_{A}\lt {m}_{B}{s}_{B}$
At $t=0,{\left(-\dfrac{dT}{dt}\right)}_{A}\gt {\left(-\dfrac{dT}{dt}\right)}_{B}$
Initially, the rate of cooling for $A$ will be higher than $B$ and temperature $(T)$ vs time $(t)$ graph will be a curve.