Two identical beakers A and B contain equal volumes of two different liquids at $60^{\circ} \mathrm{C}$ each and left to cool down. Liquid in A has density of $8 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$ and specific heat of $2000 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ while liquid in B has density of $10^{3} \mathrm{kgm}^{-3}$ and specific heat of $4000 \mathrm{JKg}^{-1} \mathrm{~K}^{-1}$. 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 · 08 Apr 2019 · Shift 1 · Heat & Thermodynamics

Two identical beakers A and B contain equal volumes of two different liquids at

6 0^{\circ} C

each and left to cool down. Liquid in A has density of

8 \times 1 0^{2} kg / m^{3}

and specific heat of

2000 Jkg^{- 1} K^{- 1}

while liquid in B has density of

1 0^{3} kgm^{- 3}

and specific heat of

4000 JKg^{- 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)

Answer: (A)

Both beakers radiate from the same surface, so the rate at which the temperature falls is set by the heat capacity per unit volume,

\frac{d T}{d t} \propto \frac{1}{ρ s}

. For liquid A,

ρ s = 8 \times 1 0^{2} \times 2000 = 1.6 \times 1 0^{6}

, while for liquid B,

ρ s = 1 0^{3} \times 4000 = 4 \times 1 0^{6}

. Because A has the smaller

ρ s

, its temperature drops faster, so its cooling curve falls more steeply from the common start at

6 0^{\circ}

C. The graph in which A cools faster than B is the correct description.

JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Single correct option