• 1.6 Brayton Cycle The Joule or Brayton cycle is shown in the P-S plane. Assuming that the working substance is an ideal gas, show that the efficiency of the cycle is Cn-Cu
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- An ideal gas at temperature T is stored in the left half of an insulating container of volume V using a partition of negligible volume (see below). What is the entropy change per mole of the gas in each of the following cases? (a) The partition is suddenly removed and the gas quickly fills the entire container. (b) A tiny hole is punctured in the partition and after a long period, the gas reaches an equilibrium state such that there is no net flow through the hole. (c) The partition is moved very slowly and adiabatically all the way to the light wall so that the gas finally fills the entire container.A monoatomic ideal gas (n moles) goes through a cyclic process shown below. Find the change in entropy of the gas in each step and the total entropy change over the entire cycle.One mole of an ideal monatomic gas is confined to a rigid container. When heat is added reversibly to die gas, its temperature changes from T1 to T2 . (a) How much heat is added? (b) What is the change in entropy of the gas?
- A great deal of effort, time, and money has been spent in the quest for a so-called perpetual-motion machine, which is defined as a hypothetical machine that operates or produces useful work indefinitely and/or a hypothetical machine that produces mole work or energy than it consumes. Explain, in terms of the first law of thermodynamics, why or why not such a machine is likely to be constructed.1. The diagram above of pressure Pversus volume Vshows a cycle of 2.0 moles of a monatomic ideal gas. aCalculate the work done cnthegs, as it expands from state 1 to state 2 b Calculane the change in intemal emngy of the gas as it epands from I to 2 e Calculate the heat added to or removed from the gas dring this exparsion from I to 2 d What is the work done on the gas from state 2 to J? What is the name of the process that happens as the gas goes from state 3 back to state 17The heat of melting of ice at 1 atmosphere pressure and 0°C is 1.4363 kcal/mol. The volume of ice is 0.0196 liter and the volume of water is 0.018 liter. If I mole of ice is melted under these conditions, what will be a. The work done in cal? b. The change in internal energy in cal? c. The change in entropy in cal? Note that 1 literxatmosphere is equal to 101.325 joule.
- a. Find an appropriate expression for the change in entropy in the following two cases: 1) S=S(T, V) 2) s= S(T, P) Where: S is entropy, T is temperature, V is volume, P is pressure b. Prove the following two themodynamie property relationships (똥),-() 8C, Where: T, P. V are temperature, pressure and volume, respectively. C, and C, are specific heats at constant volume and constant pressure, respectively.The given P-V diagram relates to a fixed quantity of CO2, assumed to be an ideal gas. The temperature at point A is 35 degrees celsius. 1. What is the total mass of CO2? 2. What is the temperature at point C in degrees celsius 3. What ist he heat added to the gas over the ABCA cycle 4. 3200 J of heat flows out of the system when the system is taken ont he straight path from C and A. What is the change in internal energy along that path?The heat of melting of ice at 1 atmosphere pressure and 0°C is 1.4363 kcal/mol. The volume of ice is 0.0196 liter and the volume of water is 0.018 liter. If 1 mole of ice is melted under these conditions, what will be a. The work done in cal? b. The change in internal energy in cal? c. The change in entropy in cal? Note Note that 1 literxatmosphere is equal to 101.325 joule. Sol": given Heat of melting ice at 1 atm pressure = 1.4363 kca kcal/ 2 = 1.4363 kcal/mole mole volume of ice = 0·0196 lts " water = 0.018 lts @ work done is define as w=pdv » w = P(V₁ hot W = 1 (0·018-00196) W = 0·0016 Cal Pay Kat Ans
- Volech 28. A monatomic ideal gas initially at pressure Po = 10° Pa, volume Vo = 0.01 m³, and temperature To = 300 K is taken through the cycle shown in the figure. p %3D ЗР. a. Determine the change in internal energy from point A to point B. b. Determine the work done by the gas from point B to point C. Po c. Determine the heat released by the gas from point C to point D. d. Determine the net work done by the gas and the net heat absorbed by the gas. Vo 3V bhe s on theAn ideal gas initially at P,, V, and T, is taken through a cycle ABCDA as shown in Figure 5. Determine in terms of P, and V, the net work done on the gas per cycle. the change in the system internal energy. the net energy added by heat to the system per cycle. 3P1 P, D. V, 3V,The work done by expansion at constant temperature To of a particular system from a V volume Vo to a volume V is given by W = NkT, In Vo We also know that, for this system, its entropy is : S = Nk- Vo (T V To 1. Calculate the Helmholtz free energy F of the system. 2. Determine the equation of state of the system. 3. Calculate the work done at an arbitrary temperature T by an expansion from volume Vo to volume V.