GATE 2021 CH – Question 54
A double-effect evaporator is used to concentrate a solution. Steam is sent to the first effect at 110 °C and the boiling point of the solution in the second effect is 63.3 °C. The overall heat transfer coefficients in the first and second effects are $2000$ and $1500\ \mathrm{W\,m^{-2}\,K^{-1}}$, respectively. The heat required to raise the temperature of the feed to the boiling point can be neglected. The heat flux in the two evaporators can be assumed to be equal. The temperature at which the solution boils in the first effect is _____ °C (round off to nearest integer).
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Correct answer: 90
Explanation
Let $T_1$ be the first-effect boiling temperature. Steam-to-first-effect driving force is $110-T_1$; first-effect vapor supplies the second effect, with driving force $T_1-63.3$.
Equal **heat fluxes** imply $U_1\Delta T_1=U_2\Delta T_2$:
$$2000(110-T_1)=1500(T_1-63.3).$$
Solving gives $3500T_1=314950$, hence $T_1=89.9857$ °C, rounded to **90 °C**. The smaller second-effect coefficient requires a larger temperature drop there.