A batch liquid with a heat capacity $(c_p)$ of $3\mathrm{.}8k\frac{J}{kg*K}$ and weighing $1,000kg$ is heated by

means of a submerged steam coil with an area $($A$)$ of $1m^2.$ The overall heat$-$transfer coefficient

$(U)$ is $600\frac{W}{m^2*K}.$ The heat loss to the surroundings can be neglected.

The appropriate differential equation that describes this heating process is:

$\frac{dT}{d}=\frac{UA}{Wc}(T_s-T)$

where: $,w=$ batch charge, $kg$

$T_s=$ steam temperature, $K$

$T=$ batch liquid temperature, $K$

$=$ time, $s$

If the liquid takes $90$min to heat from $290K$ to $360K,$ then the saturated steam temperature is

most nearly:

$($A$)360K$

$($B$)371K$

$($C$)412K$

$($D$)765K$