(1) A cycle with ideal gas operates as follows: (i) From an initial state (p₁, V₁) the gas is cooled at constant pressure to (P₁, V₂); (ii) The gas is heated at constant volume to (p₂, V₂); (iii) The gas is expanded adiabatically back to (P₁, V₁). Show that the efficiency of this cycle is η = 1 - γ (V₁/V₂) - 1 (P₂/P₁) - 1
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- Consider a heat engine with a cycle described by the figure, with the volume and pressure at points A, B, C, and D given below. VA = 0.95 × 10-3 m3VB = 3.5 × 10-3 m3PA = 2.65 × 106 N/m2PB = 2.37 × 106 N/m2PC = 0.75 × 106 N/m2PD = 1.29 × 106 N/m2 a)Calculate the net work output, in joules, of the heat engine following path ABCDA.Two moles of an ideal gas undergo an irreversible isothermal expansion fromVa=100 liters to Vb=300 liters at T=300K.(a) What is the entropy change for this process?(b) What is the Gibbs free energy change?(c) Is this process spontaneous or not? Explain your answer.(1) A thermodynamic cycle is a process, in which the system starts from initial state, goes through another state and comes back to the initial state. For the work done to the system W and heat received by the system Q, prove that W = - = -Q.
- 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.]Calculate the net work output of a heat engine following path ABCDA in the figure below, where V1 = 2.6 ✕ 10−3 m3 and V2 = 10.4 ✕ 10−3 m3.Please help me
- The figure shows a reversible cycle through which 1.00 mole of a monatomic ideal gas is taken. Process bc is an adiabatic expansion, with p, 12.0 atm and V, 3.90 x 103 m³. For the cycle, find (a) the energy added to the gas as heat, (b) the energy leaving the gas as heat, (c) the net work done by the gas, and (d) the efficiency of the cycle. (a) Number (b) Number (c) Number (d) Number Pressure Units Units Units Units Adiabatic Volume 8.001 ||||Consider the adiabatic free expansion of n moles of an ideal gas from volume V₁ to volume V2, where V₂ > V₁. [Hint: check lecture 19, chapter 5.6, process number 5. Note that such a process happens quasi-instantaneously, thus, it is irreversible.] (1) Calculate the change in entropy of the gas. (2) Calculate the change in entropy of the environment. (3) Evaluate the total change in entropy (AS = ASgas + ASenv.) for 1 mole, with V₂ = 2V/₁.A heat machine uses 1 mole ideal diatomic gas through that cycle shown in Fig. (a) Show that the ab process is isothermal compression. (b) During which process is heat absorbed by the gas? During which process is heat dissipated? How do you know? (c) Find the temperature at points a, b, and c (d) Find it engine thermal efficiency.