JEE MAIN - Physics (2019 - 8th April Morning Slot - No. 27)

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 × 102 kg/m3 and specific heat of 2000 J kg–1 K–1 while liquid in B has density of 103 kg m–3 and specific heat of 4000 J kg–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)
JEE Main 2019 (Online) 8th April Morning Slot Physics - Heat and Thermodynamics Question 319 English Option 1
JEE Main 2019 (Online) 8th April Morning Slot Physics - Heat and Thermodynamics Question 319 English Option 2
JEE Main 2019 (Online) 8th April Morning Slot Physics - Heat and Thermodynamics Question 319 English Option 3
JEE Main 2019 (Online) 8th April Morning Slot Physics - Heat and Thermodynamics Question 319 English Option 4

Explanation

We know, m = V . $$\rho$$

where, V = volume and $$\rho$$ = density.

So, we have

$${{dQ} \over {dt}} = {h \over {ms}}(T - {T_0}) = {{h(T - {T_0})} \over {V\,.\,\rho s}}$$

Since, h, (T $$-$$ T0) and V are constant for both beaker.

$$\therefore$$ $${{dQ} \over {dt}} \propto {1 \over {\rho s}}$$

We have given that $$\rho$$A = 8 $$\times$$ 102 kgm$$-$$3, $$\rho$$B = 103 kgm$$-$$3, sA = 2000 J kg$$-$$1 K$$-$$1 and sB = 4000 J kg$$-$$1 K$$-$$1, $$\rho$$AsA = 16 $$\times$$ 105 and $$\rho$$BsB = 4 $$\times$$ 106

$$\rho$$A < $$\rho$$B, sA < sB and $$\rho$$AsA < $$\rho$$BsB

$$ \Rightarrow {1 \over {{\rho _A}{s_A}}} > {1 \over {{\rho _B}{s_B}}} \Rightarrow {{d{Q_A}} \over {dt}} > {{d{Q_B}} \over {dt}}$$

So, for container B, rate of cooling is smaller than the container A. Hence, graph of B lies above the graph of A and it is not a straight line (slope of A is greater than B).

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