calculate the heat required to produce 1.7 kg of wet steam at 2000 kpa from water at 160 degrees celsius and a dryness fraction of 81%, answer in kj.
To calculate the heat required to produce wet steam, we need to consider two processes: heating the water from 160 degrees Celsius to its boiling point, and then converting it into wet steam.
First, let's calculate the heat required to raise the temperature of the water from 160 degrees Celsius to its boiling point. We can use the specific heat capacity of water, which is approximately 4.18 kJ/kg·°C.
The mass of water is 1.7 kg, the initial temperature is 160°C, and the final temperature is the boiling point of water, which is 100°C. The formula to calculate the heat required for this process is:
Q1 = m * c * (T2 - T1)
where Q1 is the heat required, m is the mass of water, c is the specific heat capacity of water, T1 is the initial temperature, and T2 is the final temperature.
Q1 = 1.7 kg * 4.18 kJ/kg·°C * (100°C - 160°C)
Q1 = 1.7 kg * 4.18 kJ/kg·°C * (-60°C)
Q1 = -401.04 kJ
Since -401.04 kJ is the amount of heat lost from the water during the cooling process (i.e., the negative sign indicates heat loss), we can find the heat gained in the next process.
Now, let's calculate the heat required to convert the water into wet steam. We can use the formula:
Q2 = m * hfg
where Q2 is the heat required, m is the mass of water, and hfg is the heat of vaporization or enthalpy of vaporization.
The heat of vaporization of water at 2000 kPa pressure can be obtained from a steam table or reference material. Let's assume it is 2392 kJ/kg.
Q2 = 1.7 kg * 2392 kJ/kg
Q2 = 4065.4 kJ
The total heat required to produce 1.7 kg of wet steam is the sum of Q1 and Q2:
Total heat = Q1 + Q2
Total heat = -401.04 kJ + 4065.4 kJ
Total heat = 3664.36 kJ
Therefore, the heat required to produce 1.7 kg of wet steam at 2000 kPa from water at 160 degrees Celsius with a dryness fraction of 81% is approximately 3664.36 kJ.