Two identical beakers A and B contain equal volumes of two different liquids at 60 ° C each and left to cool down. Liquid in A has density of 8 × 10 2 k g m - 3 and specific heat of 2000 J k g - 1 K -

Question

Two identical beakers A and B contain equal volumes of two different liquids at 60 ° C each and left to cool down. Liquid in A has density of 8 × 10 2 k g m - 3 and specific heat of 2000 J k g - 1 K - 1 while the liquid in B has density 10 3 k g 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)

TestHub · Accepted Answer

From Newton's law of cooling,
Rate of cooling: $(- \frac{d T}{d t}) = \frac{4 σ e A T_{0}^{3} (T - T_{0})}{m s}$ $\propto \frac{1}{m s}$
$∴ ρ_{A} < ρ_{B}$
$m_{A} < m_{B}$
And $s_{A} < s_{B}$
$m_{A} s_{A} < m_{B} s_{B}$
At $t = 0, {(- \frac{d T}{d t})}_{A} > {(- \frac{d T}{d t})}_{B}$
Initially, the rate of cooling for $A$ will be higher than $B$ and temperature $(T)$ vs time $(t)$ graph will be a curve.

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