Calculate the change in Gibbs and Helmholtz free energies for one mole of an ideal gas that undergoes a change in pressure from 2.0 bar to 1.0 bar at a constant temperature of 298.2K. Clearly show and state the partial derivative (sensitivity) in G that you need to integrate.
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Q: Answer in 90 minutes please.
A: Step 1: Step 2: Step 3: Step 4:
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- This is the expression valid for van der Waals gases. Calculate the final temperature if the Joule’s free expansion experiment was carried out to double the volume of 1 L gas at 25 °C with a) He b) CO2 molecules. The van der Waals coefficients, a, for He and CO2 are 0.0346 and 3.658, respectively. (Hint: Use equipartition to calculate Cv values and assume three of the vibrations not populated in carbon dioxide)According to the energy according to the equipartition theorem of degrees of freedom, what is the internal energy of 5 moles of rigid diatomic ideal gas molecules at equilibrium at temperature T?Part A: 10 moles of ideal gas initially at 10 atm and 250 K is expanded isothermally and reversibly to a final pressure of 2 atm. Calculate W, AU, and Q in Joules. Part B: The same gas in problem A, starting in the same initial state, is expanded isothermally against a constant external pressure of 2 atm, to a final pressure of 2 atm. Calculate W, AU, and Q in Joules for this irreversible process. Part C: The same gas in part B, starting in the same initial state, is expanded isothermally to a final pressure of 2 atm. The process is carried out in 4 stages. First the gas is expanded against a constant pressure of 8 atm, to 8 atm. Then the gas is expanded against a constant pressure of 6 atm, to 6 atm. Then the gas is expanded against a constant pressure of 4 atm, to 4 atm. Finally, the gas is expanded against a constant pressure of 2 atm, to 2 atm. Calculate W, AU, and Q in Joules for the 4-step process.
- A plastic bag containing 0.2 kg of water at 20°C is dropped from a height of 0.5 m onto an insulating carpet. Assume that the bag does NOT break. What is the approximate probability that a similar bag sitting on a carpet will do the reverse; that is, spontaneously jump 0.5 m in the air? Express your answer in the form "Probability = 10-x," where x is a number you will calculate. (Hint: Note that ey = 10y÷ln(10).)A container encloses 2 mol of an ideal gas that has molar mass M₁ and 0.5 mol of a second ideal gas that has molar mass M2 = 3M₁. What fraction of the total pressure on the container wall is attributable to the second gas? Note: The kinetic theory explanation of pressure leads to the experimentally discovered law of partial pressures for a mixture of gases that do not react chemically: The total pressure exerted by the mixture is equal to the sum of the pressures that the several gases would exert separately if each were to occupy the vessel alone.Obtain the most probable distribution of N molecules of an ideal gas contained in two equal and connected volumes at the same temperature by minimizing the Helmholtz free energy for the two systems.