Question

Water is being heated in a vertical piston-cylinder device. The piston has a mass of51 kg and a cross-sectional area of 100 cm2. If the local atmospheric pressure is 100kPa, determine the temperature at which the water starts boiling

Answer 1

Answer:

The temperature at which the water starts boiling is 111.35 °C.

Explanation:

First, we have to determine the total pressure experimented by water inside the piston-cylinder device. The total pressure is the sum of atmospheric and gauge pressures, the gauge pressure is the weight of piston divided by its cross-sectional area, that is:

$P_{g} = \frac{m_{p}\cdot g}{A}$

Where:

$P_{g}$ - Gauge pressure, measured in pascals.

$m_{p}$ - Mass of the piston, measured in kilograms.

$g$ - Gravitational constant, measured in meters per square second.

$A$ - Cross-sectional area, measured in square meters.

$P_{g} = \frac{(51\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{(100\,cm^{2})\cdot \left(\frac{1\,m^{2}}{10000\,m^{2}} \right)}$

$P_{g} = 50015.7\,Pa$

$P_{g} = 50.016\,kPa$

The total pressure of water is:

$P_{t} = 100\,kPa + 50.016\,kPa$

$P_{t} = 150.016\,kPa$

Temperature at which water starts boiling is the saturation temperature associated with total pressure, which can be obtained from property tables:

$T_{sat} = 111.35\,^{\circ}C$

The temperature at which the water starts boiling is 111.35 °C.