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The Ideal Gas (Module 3), Exercises of Thermodynamics

Saint Louis University (SLU)Thermodynamics

This module aims to allow you as a student to understand and determine the Ideal gas and Ideal gas laws of certain gases, and will be able to apply engineering methods in solving problems.

Typology: Exercises

2021/2022

Uploaded on 03/08/2023

benjan-torres
benjan-torres 🇵🇭

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MODULE 4 – Introduction to Ideal Gas
This module aims to allow you as a student to understand and determine the Ideal gas and Ideal gas
laws of a certain gases, and will be able to apply engineering methods in solving problems.
Ideal Gas and Ideal Gas Laws
- All gases approach the ideal gas behaviour as pressure decreases because molecules are then getting
farther apart so that forces of attraction between molecules are approaching zero, and molecules
themselves are occupying a negligible part of the volume. They are called ideal gases because they
conform with simple ideal gas laws.
Boyle’s Law
- If the absolute temperature of a given quantity of gas is held constant, the volume of the gas varies
inversely with the absolute pressure during a change of state
Charles’ Law
- If the pressure on a particular quantity of gas is held constant, then with any change of state, the
volume varies directly as the absolute temperature.
Equation of state: Characteristic Equation of perfect gas.
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MODULE 4 – Introduction to Ideal Gas This module aims to allow you as a student to understand and determine the Ideal gas and Ideal gas laws of a certain gases, and will be able to apply engineering methods in solving problems. Ideal Gas and Ideal Gas Laws

  • All gases approach the ideal gas behaviour as pressure decreases because molecules are then getting farther apart so that forces of attraction between molecules are approaching zero, and molecules themselves are occupying a negligible part of the volume. They are called ideal gases because they conform with simple ideal gas laws. Boyle’s Law
  • If the absolute temperature of a given quantity of gas is held constant, the volume of the gas varies inversely with the absolute pressure during a change of state Charles’ Law
  • If the pressure on a particular quantity of gas is held constant, then with any change of state, the volume varies directly as the absolute temperature. Equation of state: Characteristic Equation of perfect gas.

Gay-Lussac’s Law

  • If the volume of a particular quantity of gas is held constant, then with any change of state, the pressure will vary directly as the absolute temperature. For any particular state then: Pv=RT or PV=mRT or PV=nR’T Where: P= absolute pressure V= volume T= absolute temperature R= specific gas constant (R’/M.W) R= for air 287.08 J/kg-K, 53.34 ft-lbf/lb-R v= specific volume. n= number of moles = weight/ M.W M. W= Molecular weight of a given gas. R’= universal gas constant 8.3143 KJ/kgmol-K, 1545 ft-lbf/lbmol-R

Sample Problem

  1. Two vessel A and B of different sizes are connected by a pipe with a valve. Vessel A contains 142 L of air at 2,767 Kpa, 93 °C. Vessel B of unknown volume contains air at 70 KPa, 5 °C. The valve is opened and when the properties have been determined, it is found that the mixture pressure and temp and 1380 Kpa and 43 °C respectively. What is the volume of Vessel B.
  2. For a certain ideal gas R=25.8 ft-lbf/lbm-R and k=1.09 (a) what are the values of Cp and Cv? (b) what mass of this gas would occupy a volume of 15ft3 at 75 psia and 80F (c) if 30 Btu are transferred to this gas at constant volume in (b), what are the resulting temperature and pressure? Given: R=25.8 ft-lbf/lbm-R k=1.09 V1=15 ft^3 P1= 75 Psia T1=80F
  1. For a certain gas R=320 J/kg-K and Cv= .084 KJ/kg-K (a) find Cp and k (b) if 5 kg of this gas undergo a reversible non-flow constant pressure process from V1 = 1.133 m^3 and P1 =690 Kpa to a state where T 2 = 555 °C find change internal energy and change in enthalpy. Problem Set:
  2. A gas initially at 15 psia, 2 ft^3 undergoes a process to 90 psia, 0.6 ft^3 ; during which the enthalpy increases 15.45 Btu. If Cv= 0.1573 Btu/lbm-R; determine (a) Cp and R of the gas, (b) change of internal energy, BTU.
  3. A spherical balloon is 40ft in diameter and surrounded by air at 60 F and 29.92 in Hg abs. (a) if the balloon is filled with hydrogen at temp of 70 F and atmospheric pressure, what total load can it lift. (b) if it contains helium instead of hydrogen, what load can it lift?
  4. A 6m^3 tank contains helium at 127 °C and in evacuated from atmospheric pressure to a pressure of 740 mm Hg vacuum. Determine (a) mass of helium remaining in the tank (b) mass of helium pumped out (c) the temp of the remaining helium falls to 10 C, what is the pressure in Kpa? R of helium is 2077.67 J/kg-K.
  5. A reservoir contains 2.83 m^3 of CO gas at 6895 Kpa, 23.6°C. An evacuated tank is filled from the reservoir to a pressure of 3497 Kpa, 15°C. while the pressure in the reservoir decreases to 6205 Kpa and 18°C. What is the volume of the tank? MW of CO is 28.
  6. A rigid insulated tank is separated into two rooms by a stiff plate. Room A of 0.5 m^3 contains air at 250 Kpa, 300 K and room B is 1 m^3 has air at 150 Kpa, 1000 K. the plate is removed and the air comes to a uniform state without any heat transferred. find the final temp and pressure of the room.