3. Ideal and Real Gasses

What is the simplest equation of state (EOS) that relates pressure, temperature, and specific volume of a gas?

Under what conditions does the ideal gas model best approximate the behavior of a real gas?

What is a common mistake students tend to make when using the ideal gas equation of state (EOS)?

What is the primary purpose of the compressibility factor, Z?

What is the value of the compressibility factor, Z, for a gas that behaves exactly as an ideal gas?

How are reduced pressure (Pr) and reduced temperature (Tr) defined for use with the generalized compressibility chart?

According to the generalized compressibility chart, under what conditions does a real gas behave most like an ideal gas?

What is the correct procedure to determine the specific volume of a real gas using the generalized compressibility chart?

Two tanks containing methane are mixed. Tank 1 has a volume of 0.3 cubic meters at 20 degrees Celsius and 300 kPa. Tank 2 contains 1.5 kg of methane at 30 degrees Celsius and 800 kPa. If the final mixture is at 25 degrees Celsius, what is the final pressure? Methane's gas constant is 0.5182 kJ/kgK. Treat methane as an ideal gas.

1 kg of oxygen undergoes a thermodynamic cycle. In Process 1 to 2, it undergoes an isochoric process from T1 = 300 K and P1 = 1.5 atm to P2 = 3 atm. What is the temperature T2 at state 2, assuming oxygen is an ideal gas?

What is the compressibility factor Z for Methane at -50 degrees Celsius and 4.1 MPa? The critical properties for methane are Tcrit = 190.6 K and Pcrit = 4.60 MPa.

Is it reasonable to treat ammonia at 600 degrees Celsius and 500 kPa as an ideal gas? The critical properties for ammonia are Tcrit = 405.4 K and Pcrit = 11.34 MPa.

The specific volume of steam at 3 MPa and 350 degrees Celsius is determined using three methods: (1) superheated water vapour table, (2) ideal gas EOS, and (3) compressibility factor. Which method is expected to be the most accurate?

Using the ideal gas EOS, calculate the specific volume of steam at 3 MPa (3000 kPa) and 350 degrees Celsius. The gas constant for steam is 0.4615 kJ/kgK.

Calculate the specific volume of steam at 3 MPa and 350 degrees Celsius using the compressibility factor. The gas constant R is 0.4615 kJ/kgK, the critical pressure Pcrit is 22.06 MPa, the critical temperature Tcrit is 647.1 K, and the estimated compressibility factor Z is 0.94.

What does the shaded region in the T-v diagram for water (Figure 3.1.1) represent?

The ideal gas equation of state is given as Pv = RT. What does the term 'R' represent?

In the ideal gas equation PV = mRT, what units must the temperature 'T' be expressed in?

What is the defining characteristic of a real gas as opposed to an ideal gas?

Why is a generalized compressibility chart more practical to use than individual charts for each gas like hydrogen and nitrogen?

A gas which obeys the ideal gas EOS is called an ideal gas. What kind of model is the ideal gas model?

In the context of the generalized compressibility chart, what occurs at the critical point where Pr = 1 and Tr = 1?

For oxygen undergoing an isothermal expansion from state 2 to state 3 at a constant temperature of 600 K, what is the specific volume v3 at state 3 if the pressure P3 is 152 kPa? The gas constant for oxygen is 0.2598 kJ/kgK. Treat oxygen as an ideal gas.

What is the relative error when calculating the specific volume of steam at 3 MPa and 350 C using the ideal gas EOS, compared to the more accurate steam table value of 0.09056 cubic meters/kg? The ideal gas calculation yields 0.09586 cubic meters/kg.

The compressibility factor Z is defined by the equation Z = Pv/RT. What does this relationship imply?

An equation of state (EOS) is an expression that relates which three properties of a gas?

What is the final equilibrium pressure of two tanks of methane after mixing, given Tank 1 starts at 300 kPa and Tank 2 starts at 800 kPa, and the final temperature is 25 degrees Celsius? Assume ideal gas behavior.

The compressibility factor Z changes with both pressure and temperature. As pressure approaches zero, what value does Z tend to converge to?

If a substance is to be treated as an ideal gas, what should its compressibility factor be close to?

What is the key takeaway from Chapter 3 regarding the use of the ideal gas EOS?

The ideal gas equation of state can be expressed as PV = mRT. What does 'v' represent in the alternative form, Pv = RT?

Calculate the mass of methane in a 0.3 cubic meter tank at a temperature of 20 degrees Celsius and a pressure of 300 kPa. The gas constant for methane is 0.5182 kJ/kgK. Treat it as an ideal gas.

Calculate the volume of a tank containing 1.5 kg of methane at a temperature of 30 degrees Celsius and a pressure of 800 kPa. The gas constant for methane is 0.5182 kJ/kgK. Treat it as an ideal gas.

What is the key difference between how methods (1) superheated water table and (3) compressibility factor determine gas properties?

The generalized compressibility chart is valid for many substances, especially those with what kind of molecular structures?

Calculate the reduced temperature (Tr) for methane at -50 degrees Celsius. The critical temperature (Tcrit) for methane is 190.6 K.

Calculate the reduced pressure (Pr) for ammonia at 500 kPa. The critical pressure (Pcrit) for ammonia is 11.34 MPa.

For the thermodynamic cycle of oxygen described in Example 2 of Section 3.1, Process 3 to 1 is an isobaric compression. What property remains constant during this process?

If you have neither thermodynamic tables nor a real-gas EOS available, what tool can be used as a fast and reasonably accurate alternative for evaluating the properties of real gases with simple molecular structures?

For a real gas, the incorporation of the compressibility factor is intended to improve the accuracy of predicting what relationship?

Which of the following is NOT listed as a learning objective for Chapter 3?

How does the behavior of a gas change as it moves out of the 'ideal gas approximation' region on a T-v diagram towards the saturated vapor line?

What does the Key Equations section for Chapter 3 summarize?

If the compressibility factor Z for a gas is found to be 0.94, what does this indicate about its specific volume compared to an ideal gas at the same temperature and pressure?

In the process of finding the specific volume of steam at 3 MPa and 350 C, the reduced pressure (Pr) and reduced temperature (Tr) are calculated. What are their approximate values given Pcrit=22.06 MPa and Tcrit=647.1 K?

A real gas is most likely to behave like an ideal gas when its...

When using the ideal gas law PV = mRT, what is a necessary condition for the pressure P and critical pressure Pcrit when calculating reduced pressure Pr?

In the comparison of methods to find the specific volume of steam, Method 2 (ideal gas EOS) is described as easy to use but gives the least accurate result. Why is it the least accurate?

If a gas is undergoing an isochoric process and is treated as an ideal gas, what is the relationship between its initial and final states (1 and 2)?

What is the final conclusion about methane at -50 degrees Celsius and 4.1 MPa based on its calculated compressibility factor of approximately 0.78?