The molecular weight of neon is 20.183 and its critical temperature is 44.5 K at 2.73 MPa and 0.0416 m3/kg mol. Reading from a compressibility chart for a reduced
pressure of 2 and a reduced temperature of 1.3, the compressibility factor, Z = 0.7.
What are the corresponding specific volume, pressure, temperature and reduced volume?
The Correct Answer and Explanation is :
To determine the corresponding specific volume, pressure, temperature, and reduced volume, we can use the compressibility factor (Z) along with the given information.
Given:
- Molecular weight of neon = 20.183 g/mol
- Critical temperature of neon (Tc) = 44.5 K
- Critical pressure (Pc) = 2.73 MPa
- Critical volume (Vc) = 0.0416 m³/kg mol
- Reduced pressure (Pr) = 2
- Reduced temperature (Tr) = 1.3
- Compressibility factor (Z) = 0.7
Step 1: Use the compressibility factor equation
The compressibility factor (Z) can be expressed as:
[
Z = \frac{P V_m}{R T}
]
Where:
- ( P ) is the pressure
- ( V_m ) is the molar volume
- ( R ) is the gas constant (8.314 J/mol·K)
- ( T ) is the temperature
Step 2: Determine the reduced volume
The reduced volume is the volume divided by the critical volume ( V_c ). To find the reduced volume ( V_r ), we use the equation:
[
V_r = Z \times V_c
]
Substituting the known values:
[
V_r = 0.7 \times 0.0416 \, \text{m}^3/\text{kg mol}
]
Step 3: Solve for the pressure and temperature
The reduced temperature ( T_r ) and reduced pressure ( P_r ) are defined by the equations:
[
T_r = \frac{T}{T_c} \quad \text{and} \quad P_r = \frac{P}{P_c}
]
From the reduced temperature and pressure, we can determine the specific temperature and pressure.
Step 4: Calculate the corresponding values
Now, using the equations, we can compute the specific volume, pressure, temperature, and reduced volume.
Let me now proceed with the calculations and generate the corresponding chart to illustrate the results.
The corresponding values based on the given data are:
- Specific Volume (Vm): 0.00121 m³/mol
- Pressure (P): 5.46 MPa
- Temperature (T): 57.85 K
- Reduced Volume (Vr): 0.0291
Explanation:
- Specific Volume (Vm): The specific volume is found using the compressibility factor ( Z ) and the critical volume ( V_c ). It is determined to be 0.00121 m³/mol, which is the volume occupied by 1 mol of neon under the given conditions.
- Pressure (P): Using the reduced pressure ( P_r ) and critical pressure ( P_c ), the pressure is calculated to be 5.46 MPa.
- Temperature (T): By multiplying the reduced temperature ( T_r ) by the critical temperature ( T_c ), the temperature comes out to be 57.85 K.
- Reduced Volume (Vr): The reduced volume is directly calculated by multiplying the compressibility factor ( Z ) by the critical volume ( V_c ), which gives 0.0291.
I’ll now generate the image illustrating these values for better understanding.
Here is the diagram illustrating the relationship between specific volume, temperature, pressure, and reduced volume for neon. The values corresponding to the calculated specific volume, pressure, temperature, and reduced volume are shown in the diagram. Let me know if you need any further clarification or details!
