1. 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). Use the conversions 1 atm≈1 05 Pa, and 1 L-10-³ m³. РА 3 2 V (a) W₁2 == (b) W13= = (C) W₁4 = = (d) W153 == РА 1 (a) (c) V РА (b) (d) 3
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- 1. 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). Use the conversions 1 atm≈1 05 Pa, and 1 L=10-³ m³. (a) W₁2= (b) W13 (c) W14= (d) W153 = == == == ✔ (a) (C) 2 PL 39 5 (b) (d)Consider a sample of ideal gas that follow the given PV diagram. Cv= 12.5 J/mol-K and Cp = 20.5 J/mol-K. [Answer in 3 significant figures] Point A Point B Point C a) b) c) d) cycle. e) AB Isobaric Process BC Adiabatic Process CA Isochoric Process P (atm) 3.10 V (L) 4.51 1.65 T (K) 850 159 P(atm) How much work is done per cycle by the gas? 3.5 3 2.5 2 1.5 1 0.5 0 0 1 B 2 V (L) 3 How many moles of ideal gas are there? What is the temperature at point B? What is the pressure at point C? Determine how much heat is transferred to or from the environment in one complete1. 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). Use the conversions 1 atm ≈1 05 Pa, and 1 L-10-3 m³. (a) W₁2= = (b) W₁3= = (C) W₁4 = = (d) W153 = = РА PL (a) (c) 2 РА (b) (d) 3 V
- 1) A particular fluid has the fundamental equation of state S = A (N²V²E)'/5 where A is a constant. (a) Calculate the chemical potential of the fluid as a function of p and T. (b) Calculate the isothermal compressibility of this substance.Air with an initially at: P,= 920 kPa, T,= 800 K and V,= 0.13 m³, expands in a reversible adiabatic manner. If the work produced is 130 kJ. Determine a. The mass of air, in kg. b. The final pressure and temperature, in kPa and K.* ? 63. During isothermal compression, the internal energy of an ideal gas : a. Decreases b. Can go either way depending on the precise pressures and volumes c. Stays the same d. Increases 64. What is the total internal energy of a sample of 9 moles of air (considered as an ideal gas) at a temperature of 3°C? Assume that the rotational degrees of freedom are fully activated, and that the vibrational modes are "frozen out". (k=1.38 x 10-23 J/K, N-6.022x10²3) 3°C = 273+3 = 276 U= n NAF ( 1₂ KT) (9)(6.022 X 10²²) x 1.38×10²³ x 276) = 1032 a. 1.19 x 105 J b. 9.29 x 104 J c. 7.23 x 104 J d. 5.16 x 104 J 65. What is the average translational kinetic energy per oxygen molecule in this sample? a. 1.2 x 10-20 J b. 9.14 x 10-21 J c. 5.71 x 10-21 J d. 1.54 x 10-20 J 66. Is this kinetic energy the same or different from the nitrogen molecules in the sample? a. Different b. The same 67. What is the rms speed of the oxygen molecules in this sample? (the atomic mass number of oxygen is 15.994, 1 u =…
- 2 moles of a monatomic ideal gas undergoes a cyclic process as depicted in the figure below. The processes AB and CD are isobaric and the process DA is adiabat given values p= 12.5 atm, V= 5.6 L, V= 2.8 L, pc= 25 atm, and V.= 1.849 L answer the following questions. (u se R=8.314 1 atm = 1.013x 105 Pa, 1L= 10-3 m³) mol · K' Volume 1. Calculate the temperature T= 989.75 XK 2. What type of process is the process BC? adiabatic + 3. Calculate the work done by the gas in the process DA.WDA= 6765.9 XJ 4. Calculate the magnitude of the net heat entering the cycle. Q4 = 15871.96 XJ 5. Calculate the magnitude of the net heat leaving the cycle. Qe= 4593.485 XJ 6. Calculate the net work done by the gas. W= XJ 7. Calculate the thermal efficiency of the cycle. e = 8. Calculate the change in the entropy in the process AB. Include the sign (positive or negative) in your answer as well. AS AB1 moles of a diatomic ideal gas undergoes a cyclic process as depicted in the figure below. The processes AB and CD are isobaric and the process DA is adiabatic. For the given values PA= 11.5 atm, VA= 6.5 L, V3= 3.25 L, Pc= 23 atm, and Vc=1.981 L answer the following questions. J (use R=8.314 1 atm = 1.013x105 Pa, 1 L= 10-3 m3) mol · K' Volume 1. Calculate the temperature TA K 2. What type of process is the process BC? 3. Calculate the work done by the gas in the process DA.WDA = 4. Calculate the magnitude of the net heat entering the cycle. |QH|=| 5. Calculate the magnitude of the net heat leaving the cycle. |Qcl = 6. Calculate the net work done by the gas. EW= 7. Calculate the thermal efficiency of the cycle. e = 8. Calculate the change in the entropy in the process AB. Include the sign (positive or negative) in PressureThe temperature of 10 moles of an ideal gas is 1000 K. Compute the work done by the gas when it expands isothermally to three times its initial volume. Given: Boltzmann constant: k = 1.38 x 10–23 J/K, Ideal Gas Constant: R = 8.31 J/(mol K) A. 91300 J B. 9130 J C. 913 J D. 91 J E. 9 J
- 11) a) Derive an expression relating the temperature and volume for an adiabatic process of an ideal monoatomic gas for 2 different states.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…mole ideal is expanded isothermally at gas 27 °C. Its volume increases three times of initial volume. Fina the work done and heat absorbed by the R = 8.3 J mol-- K gas. Take, -1