Water in a piston/cylinder is at 100degC, x=0.5 with mass 1kg and the piston rests on two stops. The equilibrium pressure that will float the piston is 300 kPa. The water is heated to 300degC by an electrical heater.
a) At what temperature would all the liquid be gone?
I started by using the information given to find the initial specific volume. Then I considered that since all the liquid is gone, the quality would be x=1 or that the second specific volume, v_2 = v_g1.
I'm just not sure if I'm going about this question correctly.
b) Find the work and the heat transfer in the process.
To answer part a) of the question, you are on the right track in using the given information to find the initial specific volume. However, it seems you might be confusing the concept of quality with specific volume.
To begin, let's find the initial specific volume, v_1, using the given information. The specific volume can be determined using the formula:
v = V/m,
where v is the specific volume, V is the volume of the water in the piston/cylinder, and m is the mass of the water.
From the given information, we know that the mass of the water is 1 kg, and the specific volume is x = 0.5. Therefore, we can rearrange the formula to solve for V:
V = v * m = 0.5 * 1 kg = 0.5 m^3.
Now, let's move on to the condition where all the liquid is gone. At this point, the water has turned into steam and the quality, x, is equal to 1. We are looking for the temperature at which this occurs.
To determine this temperature, we can make use of a steam table or steam properties chart. These resources provide the properties of water and steam at various conditions. Look for the temperature corresponding to the saturation point where x = 1.
Keep in mind that the saturation point for steam depends on the pressure. In this case, the equilibrium pressure is given as 300 kPa. So, using the steam table or chart, look for the saturation temperature at 300 kPa when the quality is 1 (x = 1).
b) To find the work done and heat transfer in the process, we need to analyze the change in the state of water from the initial condition (100°C, x = 0.5) to the final condition (300°C, all liquid gone).
The work done, W, can be calculated as:
W = Area under the process on a P-v diagram.
To calculate this, we need to determine the specific volume at the final condition. The specific volume, v_2, when all the liquid is gone is equal to the specific volume of saturated vapor at the given pressure.
Using the steam table or chart again, find the specific volume of saturated vapor at 300°C and 300 kPa.
Once you have the specific volumes at the two states, you can calculate the work done by:
W = (P_2 - P_1) * (v_2 - v_1),
where P_1 and v_1 are the initial pressure and specific volume, and P_2 and v_2 are the final pressure and specific volume.
The heat transfer, Q, can be calculated using the first law of thermodynamics:
Q = ΔU + W,
where ΔU is the change in internal energy. For an ideal gas, internal energy is primarily influenced by temperature.
To find ΔU, calculate the change in internal energy between the initial and final states using the specific heat capacity of water. Then, substitute this value, along with the calculated work, into the first law of thermodynamics to find the heat transfer, Q.
With these steps, you should be able to find both the temperature at which all liquid is gone and the work and heat transfer in the process.