A liquid of mass 250g is kept warm in a vessel using an electric...

The expression for the rate of heat flow is,

$\dfrac{dq}{dt} = - k \left(T - {T}_{0}\right)$

Here~${T}_{0} =$Surrounding temperature

From first condition-|

$30 = - k \left(57 - 27\right)$

$⇒ k = - 1$

Using second condition-

$\dfrac{d q}{d t} = -k \left(T - {T}_{0}\right)$

but\dfrac{d q}{d t} ==ms\dfrac{d T}{d t}$</p><p>$∴ ms\dfrac{d T}{d t} = -k \left(T - {T}_{0}\right)

Substitute the given values in the above equation.

\left(\dfrac{250}{1000}\right)s \left(47 - 46 . 9\right)10 = - \left(-1\right)\left(47 - 27\right)$</p><p>$⇒ s = 8000J{kg}^{- 1}K^{- 1}$</p>$