A mass of 5kg of saturated water vapour at 200kPa is heated at constant pressure until
the temperature reaches 300oC. Calculate the work done by the steam during this process.
I found on the web that saturated water vapor @ 200 kPa had a temperature of 120.21 C and the volume was 0.88576 m^3/kg. So 5 kg will have a volume of 0.88576 m^3/kg x 5 kg = 4.4288 m^3 = V1. I was unable to find the volume at 300 C; however, assuming ideal behavior PV = nRT can be used to calculate volume @ 300 C. That gives you V2.
Then work = - p(V2-V1). The units will be in kPa*m^3 which may not be the units you want but those can be changed to what you wish.
To calculate the work done by the steam during the process, we can use the equation:
work = pressure * change in volume
First, let's calculate the change in volume. We can assume that the water vapor behaves ideally and use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the amount of substance (in this case, the number of moles of water vapor), R is the ideal gas constant, and T is the temperature in Kelvin.
Converting 300°C to Kelvin:
T = 300 + 273.15 = 573.15 K
Given that the mass of the water vapor is 5kg, we need to determine the number of moles. To do this, we can use the molar mass of water (H2O):
molar mass of water (H2O) = 2 * atomic mass of hydrogen + atomic mass of oxygen
= 2 * 1.008 g/mol + 16.00 g/mol
= 18.02 g/mol
Converting the mass from kg to grams:
mass of water vapor = 5kg * 1000 = 5000g
Number of moles of water vapor:
moles = mass / molar mass
= 5000g / 18.02 g/mol
≈ 277.2 mol
Now, let's plug the values into the ideal gas law equation:
V1 = (n * R * T1) / P1
V2 = (n * R * T2) / P2
At the initial state (pressure = 200 kPa, T = 200°C):
V1 = (277.2 mol * 8.31 J/(mol*K) * 473.15 K) / 200 kPa
At the final state (pressure = 200 kPa, T = 300°C):
V2 = (277.2 mol * 8.31 J/(mol*K) * 573.15 K) / 200 kPa
Now we can calculate the change in volume:
change in volume = V2 - V1
Next, we can calculate the work done by the steam using the formula:
work = pressure * change in volume
Let's plug in the values:
work = 200 kPa * (V2 - V1)
Finally, compute the result.