Question

A thin layer of water in field is formed after a farmer has watered it. The ambient air conditions are: temperature 20 ° C and relative humidity 5%. An extract of steam tables is given below.

Temperature (°C)	-15	-10	-5	0.01	5	10	15	20
Saturation pressure (kPa)	0.10	0.26	0.40	0.61	0.87	1.23	1.71	2.34

Neglecting the heat transfer between the water and the ground, the water temperature in the field after phase equilibrium is reached equals

1. 10.3 °C
2. -10.3 °C
3. -14.5 °C
4. 14.5 °C

Answer 1

Correct Answer - Option 3 : -14.5 °C

P_v = Partial pressure of water vapour at temperature = 20°C

Now \(\frac{{{P_v}}}{{{P_s}}} = 0.05\) (given)

∴ Form table,

P_s= 2.34 kPa

∴ P_v = 0.05 × 2.34= 0.117 kPa.

Now we have to find that temperature at which P_v become saturated pressure by interpolation method.

\(T = - 15 + \left[ {\frac{{\left( { - 10 + 15} \right)}}{{\left( {0.26 - 0.10} \right)}} \times \left( {0.117 - 0.10} \right)} \right]\)

= -15 + 0.5312

= - 14.468°C

= - 14.5°C