How much heat must be supplied to 200 kg of water at 20 degrees C to make steam at 850 kPa which is 87% dry?

To determine the total heat required to convert 200 kg of water at 20 degrees C to steam at 850 kPa with 87% dryness, a combination of steps is involved.

First, the water needs to be heated from its initial temperature of 20 degrees C to the boiling point at 850 kPa. The saturation temperature at this pressure can be found using steam tables or thermodynamic properties, which typically reveal a saturation temperature around 179.9 degrees C. The specific heat of water is approximately 4.18 kJ/kg·°C, allowing us to calculate the heat required to raise the temperature:

( Q_1 = m \cdot c \cdot \Delta T )

Where:

• ( m ) = mass of water (200 kg)

• ( c ) = specific heat of water (4.18 kJ/kg·°C)

• ( \Delta T ) = change in temperature (179.9 - 20) degrees C

Next, we need to account for the heat required to convert the liquid water at 179.9 degrees C to saturated steam. The enthalpy of vaporization at this pressure can be determined from the steam tables. The total heat