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 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.]

A cylinder containing n mol of an ideal gas undergoes an adibatic process. Starting with dW = pdV and using the condition pVY = constant, show that the work done by the gas: 1 W × (p;V; - PfV¢) %3D Starting from the first law of thermodynamics in differential form, prove that the work done by the gas is n×Cy(T; - Tf).

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.

A 4.00 L sample of a diatomic ideal gas with specific heat ratio 1.40, confined to a cylinder, is carried through a closed cycle. The gas is initially at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. (d) Find the temperature at the end of the cycle. K   (e) What was the net work done on the gas for this cycle?J

A rigid box contains 0.9 mol of an ideal monoatomic gas. Heat is added to the gas and its temperature changes from 183 K to 295 K. If this is a reversible process, what is the change in entropy of the gas in J/K?

a) Consider a process involving an ideal diatomic gas with n = 3mol, following p = aV, where a = 1 x 105 Pa/m³ is a constant. The gas ex- pands from volume V; = 1 m³ to V; = 4m3. P2 Find the (i) work done on the gas. (ii) heat entering the gas. 1 (iii) change in the internal energy of the gas. b) Now consider the cycle depicted in the figure, involving the same amount of gas as in the previous part. A → B is the process described in the previous subtask, B → C an isochor and C → A an isobar. Additionally, V2/V1 = n = 4 and Vi = 1 m³. Find the Pi 3 i) work done by the gas during one loop of the cycle. V1 V2 V ii) thermal efficiency of the cycle. iii) maximum theoretical efficiency of a Car- not cycle having the same temperature extrema as in this cycle. iv) coefficient of performance of the cycle, if it were used as a refrigerator .

One mole of an ideal gas, for which CV,m = 3/2R, initially at 298 K and 1.00 × 10^5 Pa undergoes a reversible adiabatic compression. At the end of the process, the pressure is 1.00 × 10^6 Pa. Calculate the final temperature of the gas. Calculate q, w, ΔU, and ΔH for this process.