thermodynamics lecture 1 sengel bkkkkkook

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1. Thermodynamic-II Lecture-1

2. Today’s lecture…. Composition of non reacting gases. Mole fraction. Mass fraction. Volume fraction. Delton’s Law of partial pressure. Amagat’s Law

3. Composition of a gas mixture The composition of a gas mixture refers to the relative amounts or proportions of different gases that make up the overall mixture. This composition is often expressed using various metrics such as mole fraction, mass fraction, or volume fraction. Let's explore an example to illustrate the concept of gas mixture composition: Air is a common example of a gas mixture. It is composed of several gases, with nitrogen (N₂) and oxygen (O₂) being the primary components. Other gases, such as carbon dioxide (CO₂), argon ( Ar ), and trace amounts of other gases, are also present.

4. Composition of a gas mixture

5. Perfect gases Perfect gases generally refers to an idealized model of gases that follows ideal gas laws . In the ideal gas model, gases are assumed to consist of particles (atoms or molecules) that are in constant, random motion, and the interactions between these particles are negligible. It's important to note that real gases deviate from ideal behavior under certain conditions, such as at high pressures or low temperatures. In reality , no gas is truly perfect according to the ideal gas laws under all conditions.  

6. Properties of an ideal gas mixture Each gas in the mixture behaves independently of the others. The total pressure of the ideal gas mixture is the sum of the partial pressures of each gas. P total ​ = P 1 + ​ P 2 + P 3 +……..+ P n The total volume of the ideal gas mixture is the sum of the volumes that each gas would occupy individually at the same temperature and pressure. Ideal gas mixtures assume that there are no intermolecular forces or interactions between gas molecules. This implies that the gases do not condense into liquids or exhibit deviations from ideal behavior.

7. Mole Fraction Mole fraction (​ ) is the ratio of moles of a specific gas to the total moles in the mixture. ​ = ​​ Mole fractions are essential for quantifying the proportion of each gas in the mixture, aiding in comprehensive composition analysis. Mole fraction of  = Mole fraction of  =  

8. Mass fraction Mass fraction refers to the proportion of the total mass of a specific gas component in a mixture of gases. The mass fraction is a measure of the concentration of a particular gas within the overall gas mixture. It is calculated by dividing the mass of the individual gas ( ) by the total mass ( ) of the gas mixture. = ​​ For a mixture of non-reacting gases, the sum of the mass fractions of all individual gases should equal 1. This reflects the fact that the total mass of the mixture is distributed among the different gas components.  

9. Volume Fraction: The volume fraction is the ratio of the volume of each gas to the total volume of the mixture. In the case of air, the approximate composition by volume is often given as about 78% nitrogen, 21% oxygen, 0.04% carbon dioxide, and trace amounts of other gases.

10. Dalton's Law of Partial Pressures According to Dalton's Law, the total pressure exerted by a mixture of non-reacting gases is the sum of the partial pressures of individual gases. P total ​ = P 1 + ​ P 2 + P 3 +…….. P n This law is particularly useful when dealing with gas mixtures, providing a straightforward method to calculate the contribution of each gas to the total pressure.

11. Example Suppose you have a container that contains a mixture of three non-reacting gases: nitrogen (N₂), oxygen (O₂), and carbon dioxide (CO₂). Each gas exerts its own pressure within the container. According to Dalton's Law: P total =P N₂​ + P O₂​ + P CO₂​ P N₂ ​= 400 kPa; P O₂​ = 300 kPa; P CO₂​ ​= 300 kPa P total = 400 kPa + 300 kPa + 300 kPa = 1000 kPa

12. Problem:1 You have a container containing a mixture of two non-reacting gases: oxygen (O₂) and nitrogen (N₂). The total pressure in the container is 800 kPa, and the mass fraction of oxygen in the mixture is 0.4. Determine: The mass fraction of nitrogen in the mixture? The mass of oxygen in the container if the total mass of the mixture is 5 kg?

13. Solution Mass Fraction of Nitrogen ( ): = 1 ​= 1−0.4 = 0.6 Mass of Oxygen in the Container: = = 0.4×5  

14. Problem:2 You have a container containing a mixture of three non-reacting gases: hydrogen (H₂), carbon dioxide (CO₂), and nitrogen (N₂). The partial pressures of these gases are as follows: P H₂​ = 150kPa; P CO₂ = 200 kPa; P N₂ = 100 kPa. The molar masses of the gases are: M H₂ = 2 g/mol; M CO₂ = 44 g/mol; M N₂ = 28 g/mol. if the container volume is 5 L and the temperature is 300 K. Calculate: The mole fraction of each gas in the mixture. The mass fraction of each gas in the mixture.

15. Solution = Use the ideal gas law to find the moles of each gas ( n i ​): ​= ​ Where R =8.314 J/(mol K) Is the ideal gas constant. = ​​  

16. Amagat's law The volume occupied by a mixture of non-reacting gases is equal to the sum of the volumes of the individual gases at the same temperature and pressure as the mixture. ​ = ​ This law is applicable on the non-reacting gases where there are no significant intermolecular forces between the gas molecules. It's essential to note that Amagat's law is most accurate under conditions where gases behave ideally, and it becomes less precise under extreme conditions (high pressure, low temperature) or when gases have significant interactions with each other.  

17. Example Let's say you have a container of nitrogen gas (N₂) and a container of argon gas ( Ar ). According to Amagat's law, the total volume of the gas mixture, assuming ideal behavior, would be the sum of the volumes of nitrogen and argon individually. = ​ It's essential to note that Amagat's law is most accurate under conditions where gases behave ideally, and it becomes less precise under extreme conditions (high pressure, low temperature) or when gases have significant interactions with each other.  

18. Adiabatic mixture of perfect gases The adiabatic mixture of perfect gases refers to a scenario where a mixture of perfect gases undergoes an adiabatic process. An adiabatic process is one in which there is no heat exchange with the surroundings. represents the ratio of the specific heat at constant pressure to the specific heat at constant volume. For a mixture of perfect gases, each gas component in the mixture follows its own adiabatic process, and the overall behavior is determined by the combined effect of these individual processes.  

19. The adiabatic process equations are commonly used to analyze the changes in temperature, pressure, and volume of a gas mixture when no heat is transferred to or from the system. This can be relevant in various applications, such as in the analysis of processes in internal combustion engines, compressors, and other thermodynamic systems where heat exchange with the surroundings is minimal. It's worth noting that the adiabatic process assumes that the system is insulated from its surroundings, and any changes in internal energy are solely due to work done on or by the system.

20. Adiabatic Compression in a Compressor: Initial State: Air enters the compressor at a certain temperature, pressure, and volume. The compressor compresses the air adiabatically, meaning that no heat is exchanged with the surroundings. Compression: As the air is compressed, its volume decreases, and its pressure and temperature increase. The adiabatic compression process can be described by the adiabatic equation , where P is the pressure, V is the volume, and γ is the ratio of specific heats. Final State: The air exits the compressor at a higher pressure, temperature, and potentially a different volume.