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?

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?

• A. 2,039.4 kJ
• B. 407,880 kJ
• C. 1,774.28 kJ
• D. 484,507.6 kJ

Answer: (D)

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

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