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- In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat. Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5. Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas. A) Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion. Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0. p(V) = __________ B) At the end of the adiabatic expansion, the gas fills a new volume V1, where V1>V0. Find W, the work done by the gas on the container during the expansion. Express the work in terms of p0, V0, and V1. Your…An ideal gas expands quasi-statically and isothermally from a state with pressure p and volume V to a state with volume 4V. How much heat is added to the expanding gas?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.
- A dilute gas expands quasi-statically to three times its initial volume. Is the final gas pressure greater for an isothermal or an adiabatic expansion? Does your answer depend on whether the gas is monatomic, diatomic, or polyatomic?A monatomic ideal gas undergoes a quasi-static process that is described by the function pV=p1+3(vv1) , where the stating state is (p1,v1) and the final state (p2,v2) . Assume the system consists of n moles of the gas in a container that can exchange heat with the environment and whose volume can change freely. (a) Evaluate the work done by the gas during the change in the state. (b) Find the change in internal energy of the gas. (c) Find the heat input to the gas during the change. (d) What ale initial and final temperatures?The temperature of n moles of an ideal gas changes from T1 to T2 in a quasi-static adiabatic transition. Show that the work done by the gas is given by W=nR1(T1T2).
- When 400 J of heat are slowly added to 10 mol of an ideal monatomic gas, its temperature rises by 10 . What is the work done on the gas?If 9.50 moles of a monatomic ideal gas at atemperature of 235 K are expanded isothermally from a volumeof 1.12 L to a volume of 4.33 L, calculate (a) the work done and while the system performs 120 J of work on its surroundings. Howmuch heat was added to the system?You use a 32 L chamber to hold 11.2 g of Neon gas at 297 K, and then allow the gas to expand reversibly and isothermally until its volume has increased by 2.1 L. Calculate w, then use the properties of an ideal gas to determine ΔU, and finally determine q by applying the 1stLaw of Thermodynamics.
- One very special method for performing work is to do so reversibly. A change of state occurs reversibly if the external pressure equals the gas pressure throughout the change of state. If the change of state occurs isothermally (at constant temperature), then the expression for reversible work on an ideal gas is: w= -nRTln(V2/V1) A 4.00-mol sample of an ideal gas, initially at 331 K and occupying a volume of 3.4 L, does 2,765 J of isothermal reversible work on the surroundings. What is the final volume (in L)? Round your answer to the tenths (0.1) place.From a work-production perspective, which is more valuable: (a) thermal energy reservoirs at 675 K and 325 K or (b) thermal energy reservoirs at 625 K and 275 K?How would the temperature of a REAL gas (not perfect) in a reversible adiabatic expansion be affected?