# Two identical beakers A and B contain equal volumes of two different liquids at $60^{o}C$ each and left to cool down. Liquid in A has density of $8\times 10^{2}kg/m^{3}$ and specific heat of $2000\; J\; kg^{-1}K^{-1}$ while liquid in B has density of $10^{3}\; kg\: m^{-3}$ 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)Option 1)Option 2)Option 3)Option 4)

From given

$\rho _{A}< \rho _{B},$

$\Rightarrow m _{A}

and $\Rightarrow s _{A}

By newtons law of cooling

$\frac{-dT}{dt}=\frac{4\: \sigma\: e\: A\: T{_{0}}^{3}(T-T_{o})}{ms}$

$\Rightarrow \frac{-dT}{dt}\alpha \frac{1}{ms}$

at $t=0$

$-(\frac{dT}{dt})_{A}\alpha \frac{1}{m_{A}s_{A}}$

$-(\frac{dT}{dt})_{B}\; \alpha \frac{1}{m_{B}s_{B}}$

and we know

$m_{A}s_{A}

So slope of T v/s t curve for A is more than B.

Option 1)

Option 2)

Option 3)

Option 4)

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