On the PV diagram for an ideal gas, one isothermal curve and one adiabatic curve pass through each point. Prove that the slope of the adiabat is steeper than the slope of the isotherm by the factor y.
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- Find the work done in the quasi-static processes shown below. The states are given as (p, V) values for the points in the PV plane: 1 (3 atm, 4 L), 2 (3 atm, 6 L), 3 (5 atm, 4 L), 4 (2 atm, 6 L), 5 (4 atm, 2 L), 6 (5 atm, 5 L) and 7 (2 atm, 5 L).A monatomic ideal gas undergoes a quasi-static adiabatic expansion in which its volume is doubled. How is the pressure of the gas changed?Two moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with a pressure of 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state. (c) Find work done by the gas in the process. (d) Find the change in internal energy in the process. Assume Cv=5R and Cp=Cv+R for the diatomic ideal gas in the conditions given.
- On the PV diagram for an ideal gas, one isothermal curve and one adiabatic curve pass through each point as shown. Prove that the slope of the adiabatic curve is steeper than the slope of the isotherm at that point by the factor γ.When an ideal gas undergoes a quasistatic adiabatic volume change, its pressure p and volume V are related by PVY = a constant, where y is the ratio of the molar specific heats for the gas. Start from the first law of thermodynamics, present a proof of this equation.Compare the charge in the internal energy of an ideal gas for a quasi-static adiabatic expansion with that for a quasi-static isothermal expansion. What happens to the temperature of an ideal gas in an adiabatic expansion?
- A sample of an ideal gas consists of 1000 molecules, each with 3 degrees of freedom. The gas is at a temperature of 300 K. Calculate the total internal energy of the gas using the Equipartition theorem.The volume of a monatomic ideal gas doubles in an adiabatic expansion. By what factor do (a) the pressureCalculate the values of q, w, delta U, and delta H for the reversible adiabatic expansion of 1 mole of a monatomic ideal gas from 5.00m^3 to 25 m^3. The temperature of the gas is initially 298K.
- In a cylinder, 1.20mol of an ideal monatomic gas, initially at 3.60×105Pa and 300K, expands until its volume triples. Compute the work done by the gas if the expansion is adiabatic. I need a thorough explanation as to HOW to do it. I know that: W = -nCv(Delta T) In another solution, someone said W = -nCvT1(1-(1/3)^2/3).......why??? I need to understand it.Problem 2: A bubble of CO2 forms at the bottom of a lake and rises to the surface. Recall that the pressure P below the surface of a lake increases with depth h as AP = pg Ah, where p is the density of the water. As the bubble rises, the pressure decreases and the bubble expands. If the bubble rises slowly, the process is isothermal. But if the bubble rises rapidly, the process is adiabatic. You can assume f= 6 for CO2 gas near room temperature (3 translational modes and 2 rotational modes and one active bending mode.) a) Compare two initially identical bubbles A and B: Bubble A rises adiabatically, and bubble B rises isothermally. Let Pı be the pressure at the bottom of the lake and P2 be the pressure at the top of the lake. For each of the bubbles, A and B, derive a formula for the ratio of the volumes V2/V1 , and predict which bubble will expand more as it rises. b) For each bubble, A and B, by what factor will the volume increase if the bubble starts at a depth of 100 m and rises…Compare the charge in the internal energy of an ideal gas for a quasi-static adiabatic expansion with that for a quasi-static isothermal expansion?