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Q: Consider a process that uses n moles of a monatomic ideal gas operating through a Carnot cycle. The…
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With n = 1 mol of ideal gas, a cycle consisting of two isobars and two isochoric processes takes place. In cases 1 and 3, the temperature of the gas is T1 = 400K and T3 = 900K. It is known that states 2 and 4 exist on the same isothermal curve. Find the work that the ideal gas does in this cycle.


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- Consider a monatomic ideal gas operating through the Carnot cycle. The initial volume of the gas is V1 = 160 × 10-3 m3. During the isothermal compression step, the volume of gas is reduced by a factor of 4. In the adiabatic heating step, the temperature of the gas is doubled. What is the volume at point 3, in cubic meters? a. During the isothermal compression step, the volume of gas is reduced by a factor of 4. In the adiabatic heating step, the temperature of the gas is doubled. What is the volume at point 3, in cubic meters? b. What is the volume at point 4, in cubic meters?Question B: A sample of 1.00 mole of a diatomic ideal gas is initially at temperature 265 K and volume 0.200 m3. The gas first undergoes an isobaric expansion, such that its temperature increases by 110.0 K. It then undergoes an adiabatic expansion so that its final volume is 0,440 m3. i. Sketch a PV diagram for the two-step process, including labeled initial, final, and intermediate states, and a two-part curve/path with an arrow indicating direction. Label the initial state "i", the final state "f", and the intermediate state "b". Write down the known values for P, T, and V at each point, e.g. T; = 265 K, and Th = 375 K. (B.1) What is the initial pressure of the gas, Pi, in pascals [Pa]? Pi = Pa Enter a number. (B.2) What is the total heat transfer, Q, to the gas, in joules [J]? Q = Qtotal = (B.3) What is the total work done on the gas, w, in joules [J]? w = Wtotal = Enter your answer for problem (B.3) for credit. First, use the following questions as intermediate steps; answers can…Consider the following thermodynamic cycle for an ideal gas: From A to B the gas is compressed adiabatically. From B to C heat Qh is added to the gas and the gas is kept at constant volume. From C to D the gas expands adiabatically. From D to A the gas ejects heat Q₁ to the environment and is kept at constant volume. (1) Draw the PV-diagram associated to this cycle. (2) Show that the efficiency of an engine running this cycle is given by e = 1 - (3) Calculate the efficiency for a compression ratio VA/VB = 8 assuming a diatomic gas. [Hint: for a diatomic gas Cv = (5/2)R.]
- Consider a process that uses n moles of a monatomic ideal gas operating through a Carnot cycle. The initial temperature and pressure of the gas are T1 and P1, respectively. Consider steps 1 → 2, 2 → 3, 3 → 4, and 4 → 1. a. In the adiabatic heating, the temperature of the gas is doubled. Write an expression for the volume V3 after this step in terms of V1. b. Write an expression for the volume V4 in terms of V1.A certain gasoline engine is modeled as a monatomic ideal gas undergoing an Otto cycle, represented by the p-V diagram shown in the figure. The initial pressure, volume, and temperature are p1 = 1.05 × 105 Pa, V1 = 0.035 m3, and T1 = 290 K, respectively. a)The first step in the Otto cycle is adiabatic compression. Enter an expression for the work performed on the gas during the first step, in terms of V1, V2, and p1. b) Calculate the temperature of the gas, in kelvins, at the end of the first step. c)The fourth and last step in the Otto cycle is isochoric cooling to the initial conditions. Find the amount of heat, in joules, that is discharged by the gas during the fourth step.Please use the W=nRTln(V2/V1) equation.
- An ideal gas undergoes the thermodynamic process shown in the ??PV diagram in the figure. Determine whether each of the values (a) Δ?ΔU, (b) ?W, (c) ?Q for the gas is positive, negative, or zero. (Note that ?W is the work done ??on the gas.) Hint: First use the ideal gas law to find the initial and final temperatures in terms of ?0P0 and ?0V0 and determine if the final temperature is greater than, less than, or equal to the initial temperature. (a) ΔU A.+ B.- C.0 (b) W A.+ B.- C.0 (c) Q A.+ B.- C.0You 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?