Question

A tank of compressed air of volume 1.00 m³ is pressurized to 22.4 atm at T = 273 K. A valve is opened, and air is released until the pressure in the tank is 13.7 atm. How many molecules were released? Boltzmann constant is 1.38 × 10⁻²³ J/K.

How long will the air in the tank last at 22.2 m?

___min

Answer 1

Answer: (Note: Here answer was given for part-A only. Try asking Part-b separately.)

Concept: As we know the temperature is based on the thermal equilibrium concept. Let we suppose that two systems are allowed to exchange energy. So, The net flow of energy is always from the system at high temperature to the system at the lowest temperature. As energy flows, the temperature of the two systems approach one another. When the temperature are the same, there is no longer any net flow of energy. So, the objects are now said to be in thermal equilibrium. Heat is define as the energy that flows between two objects or systems due to a temperature difference between them. Thermodynamics consists of four main laws. Zeroth law of Thermodynamics: If two objects are each in thermal equilibrium with a third object, then the two are in thermal equilibrium with one another. As we know, Without the zeroth law, it will be impossible to define temperature. We use more than one scale to measure the temperature. The conversion between the Fahrenheit degree and the Celsius degree is ATF = ATC x 1.8 °F/°C +32 °F The conversion between the Celsius degree and the Fahrenheit degree is Tp-32 F Tc = 1.8 FC The conversion between the Kelvin degree and the Celsius degree is T=Tc + 273.15 In order to evaluate the linear expansion. We use the following relation: AL = QAT

Where, AL is the elongation in the string. Lo is the initial length, a is the coefficient of the linear expansion and AT is the changing in temperature, According to Charles's law. At constant pressure: ᏙᎢ At constant volume. According to Gay-lussac's law: PaT At constant temperature, According to Boyle's law: So, The ideal gas equation for microscopic world assigns that PV = NET Where, k = 1.38 x 10-23 J/K is the Boltzmann's constant. Also, The ideal gas equation for macroscopic world assign's that PV = nRT Where, R = Navok is the universal gas constant and n is the number of moles.

Where, R = NAvok is the universal gas constant and n is the number of moles. For two cases, We use the following equation: Calculation: As we mention before in the concept session. The ideal gas equation for microscopic world assigns that PV = NKT Divide both sides by KT. Then we get PV N = RT We shell use the changing in the pressure, Then we get AN APV AN= IT 1 m x 13.7atm-22.4 atm) 1.38 x 10-23 J/K x 273 K* x 1.013 x 10 Pa/atm = -2.419 x 1026 Result: AN = -2.419x 1026