Problem 5.4: For each of the following conditions, compute (i) the mechanical work w done by a sample of dry air, and (ii) the heat q added to the sample. a) Isothermal compression to one-fifth of its original volume at 15°C. -1 -1 Answer: (i) -1.3 × 105 J kg-¹ (ii) -1.3 × 105 J kg-¹ b) Isobaric heating from 0°C to 20°C. Answer: (i) 5.7 x 103 J kg-¹ (ii) 2.0 × 104 J kg-1 x
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- 1 kg of air is reversibly heated at constant pressure from an initial state of 300 K and 1 bar until its volume increases to three times its initial value. Determine the internal energy changes, entapy, and heat and work requirements for this process. The molar mass of air is 28.9 g / mol. Write down all your assumptions made. w= dU= dH= Q=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. ? JLook at the P-V diagram below (Diagram 1). Calculate the work done by the gas for the paths A, B and C. Assume that in Diagram 1, P1 = 1 atm, P2 = 4 atm, V1 = 5 L, V2 = 15 L. a) WA = 1013 J, WB = 0, WC = -2533 J b) WA = 0.01 J, WB = 0, WC = -0.025 J c) WA = 2533 J, WB = 0, WC = -1013 J Calculate the work done by the gas for the path AB in Diagram 2. Use the data: P1 = 1 atm, P2 = 4 atm, V1 = 5 L, V2 = 20 L. (Path AB is an "isothermal" which means the temperature T is constant on this path). a) 0.012 J b) 1220 J c) 0.0278 J d) 2809 J
- Find the total change in the internal energy of a gas that is subjected to the following two-step process. In the first step the gas is made to go through isochoric heating until it gains 5963 J and its pressure is 2.72 105 Pa. In the second step it is subjected to isobaric adiabatic compression until its volume decreases by 7.30 10-3 m3. What is the total change in internal energy of this gas?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 five and the volume by a factor of four. 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.)Problem #2: For this problem, one mole of a diatomic ideal gas is taken around a reversible cycle by starting at pressure P, volume V, and temperature T, then in an isochoric process 1 increasing pressure to 6P, then in an isobaric process 2 increasing its volume to 21V, then another isochoric process 3 back to a pressure P, and finally in an isobaric process 4 back to P, V, T. Find the temperature of this gas at the end of process 1, 2, and 3 in terms of the original temperature T. Find the internal energy change in process 1 and in process 2 in terms of P and V. Find the heat transfer in process 1 and in process 2 in terms of P and V.
- Problem 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.two canisters A and B each contain 0.20 mol of a diatomic gas at 400k and a pressure of 405300 Pa. A expands isothermally and B adiabatically until pressure of each is 303975 Pa. [for a diatomic gas Cv = (2/5) R 1) Sketch both processes on a single PV diagram 2) What are the final temperature and final volume of each canisterYou 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?For a refrigerator let us consider the following quantities: The absolute value of the amount of heat that a refrigerator absorbs from the cold reservoir (its internal part): |Q₁| The absolute value of the amount of heat that the refrigerator releases to the environment: |Q₂1. We can state that: a) 1Q₁1=1Q₂1 b) 1Q₁1>1Q₂1 c) IQ₂|>1Q11 d) whether | Q₁ | is greater than, less than or equal to Q₂ | depends on the performance of the cooler.