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A monoatomic ideal gas is taken through the cycle A→B→C→A shown in the figure. Express all the answers below in terms of p0 and V0.
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Find the work WA→B done by the gas during process A → B. Find the heat QA→B flowing into the gas during the process A → B. |
| Find the work WB→C done by the gas during the process B → C. |
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- A container is filled with an ideal diatomic gas to a pressure and volume of P1 and V1, respectively. The gas is then warmed in a two-step process that increases the pressure by a factor of two and the volume by a factor of three. Determine the amount of energy transferred to the gas by heat if the first step is carried out at constant volume and the second step at constant pressure. (Use any variable or symbol stated above as necessary.)A gas expands from I to F in the figure below. The energy added to the gas by heat is 302 J when the gas goes from I to Falong the diagonal path. Three paths are plotted on a PV diagram, which has a horizontal axis labeled V(liters), and a vertical axis labeled P (atm). The green path starts at point I (2,4), extends vertically down to point B(2,1), then extends horizontally to point F (4,1). The blue path starts at point I (2,4), and extends down and to the right to end at point F (4,1). The orange path starts at point I(2,4), extends horizontally to the right to point A (4,4), then extends vertically down to end at point F(4,1). (a) What is the change in internal energy of the gas?J(b) How much energy must be added to the gas by heat for the indirect path IAF to give the same change in internal energy?JConsider the following two-step process. Heat is allowed to flow out of an ideal gas at constant volume so that its pressure drops from P₁ = 2.7 atm to P2 = 1.7 atm. Then the gas expands at constant pressure, from a volume of V₁ = 5.9 L to V₂ = 9.6 L, where the temperature reaches its original value. See the figure ( Figure 1). Figure P P₁ P2 σ P D HÅ AU = Value Units Submit Request Answer Part C 1 of 1 wwwww ? Calculate the total heat flow into or out of the gas. Express your answer to two significant figures and include the appropriate units. ☐ με Value Units Submit Request Answer
- The heat engine shown in the figure uses 2.0 mol of a monatomic gas as the working substance. (Figure 1) Figure p (kPa) 600 400 200 0 0 0.025 0.050 < 1 of 1 V (m³) Part D Determine AEth, Ws, and Q for 3→1. Enter your answers numerically separated by commas. Express your answer using two significant figures. VE ΑΣΦ AEth, Ws, Q = Submit Part E Request Answer What is the engine's thermal efficiency? Express your answer using two significant figures. ? JProblem 4: Consider a cylinder with a movable piston containing n moles of an ideal gas. The entire apparatus is immersed in a constant temperature bath of temperature T Kelvin. The piston pushes slowly outward on an external body which matches the force momentarily at each instant so that the gas expands quasi-statically from a volume V1 to V2 at constant temperature T. The isothermal process is shown in the figure above, where the pressure p is related to the volume V by the ideal gas law as follows: pV = nRT, where R is the gas constant. Part (b) For n = 3 moles, T = 350 K, and V2 = 2.5V1, determine the work done by the gas on the external body. The gas constant is R = 8.314 J K-1 mol-1.A particular thermodynamic cycle acting on a monatomic ideal gas (y = 1.67) includes an isobaric expansion, an isochoric cooling, and then a isothermic contraction. The PV diagram is shown in the image below. P V The isobaric expansion occurs at a pressure of 1.8 × 105 Pa and changes the volume of the gas from 6.7 x 10-2 m³ to 13.08 × 102m³. What is the efficiency of the process?
- A system consisting of an ideal gas contained in a cylinder with a frictionless piston is taken around the closed path a → b→ c → a as shown in figure 1 where the process c → a is isothermal. During the closed cycle, the system expels 100 J to the environment. If the heat expelled by the system during the isobaric leg b → c of the cycle is 300 J, what is the change in internal energy ∆U during the process a → b? Note: Include the sign and make clear whether heat is expelled or absorbed by the system.You would like to raise the temperature of an ideal gas from 295 K to 960 K in an adiabatic process. a)What compression ratio will do the job for a monatomic gas? b)What compression ratio will do the job for a diatomic gas?Part A: If you supply 2950 J of heat to 6.00 moles of an ideal diatomic gas initially at 23.0 ∘C in a perfectly rigid container, what will be the final temperature of the gas? Express in degrees Celsius. Part B: Suppose the gas in the container were an ideal monatomic gas instead. How much heat would you need to add to produce the same temperature change? Part C: Which pV diagram expresses these processes?