GATE Papers >> Mechanical >> 2016 >> Question No 55

Question No. 55 Mechanical | GATE 2016

For water at $\begin{array}{l}25^\circ C\\\end{array}$, $dp_s/dT_s$= 0.189 kPa/K ($p_s$ is the saturation pressure in kPa and $T_s$ is the saturation temperature in K) and the specific volume of dry saturated vapour is 43.38 $\mathrm m^3/\mathrm{kg}$. Assume that the specific volume of liquid is negligible in comparison with that of vapour. Using the Clausius-Clapeyron equation, an estimate of the enthalpy of evaporation of water at $25^\circ\;\mathrm C$ (in kJ/kg) is __________


Answer : 2400 : 2500

Solution of Question No 55 of GATE 2016 Mechanical Paper

Clauses-Clapeyeon equation

$ \begin{array}{l}\frac{\partial{\mathrm P}_\mathrm s}{\partial{\mathrm T}_\mathrm s}=\frac{{\mathrm h}_\mathrm{fg}}{{\mathrm T}_\mathrm s\times\left({\mathrm V}_\mathrm g-{\mathrm V}_\mathrm f\right)}\\0.189=\frac{{\mathrm h}_\mathrm{fg}}{298\times43.38}\;\;\;\;\;\;\;\left[\because{\mathrm V}_\mathrm g\gg{\mathrm V}_\mathrm f\right]\\\therefore{\mathrm h}_\mathrm{fg}=2443.248\mathrm{kJ}/\mathrm{kg}\end{array} $

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