Consider a reversible cycle involving two isobaric and two isochoric (iso-volumic) processes, operating over ranges in volume of 2-5 m³ and pressure of 2-5 atm. The cycle uses 100 mol of an ideal gas for which the internal energy is given as U = nRT. a) Draw the cycle in a fully-labelled P-V indicator diagram, indicating the direction if operated as a heater, and label the corners of the cycle with the temperatures of the gas. b) Calculate the efficiency of the cycle if operated as a heater.

An ideal gas with specific heat ratio confined to a cylinder is put through a closed cycle. Initially, the gas is at Pi, Vi, and Ti. First, its pressure is tripled under constant volume. It then expands adiabatically to its original pressure and finally is compressed isobarically to its original volume. (a) Draw a PV diagram of this cycle. (b) Determine the volume at the end of the adiabatic expansion. Find (c) the temperature of the gas at the start of the adiabatic expansion and (d) the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle?

Two moles of a monatomic ideal gas such as helium is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with pressure 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state of the gas. (c) Find the work done by the gas in the process. (d) Find the change in internal energy of the gas in the process.

It is unlikely that a process can be isothermal unless it is a very slow process. Explain why. Is the same true for isobaric and isochoric processes? Explain your answer.

An idealized diesel engine operates in a cycle known as the air-standard diesel cycle shown in Figure P18.48. Fuel is sprayed into the cylinder at the point of maximum compression, B. Combustion occurs during the expansion B C, which is modeled as an isobaric process. Show that the efficiency of an engine operating in this idealized diesel cycle is e=11(TDTATCTB) Figure P18.48.

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.

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), 6 (5 atm, 5 L) and 7 (2 atm, 5 L).

At point A in a Carnot cycle, 2.34 mol of a monatomic ideal gas has a pressure of 1 4000 kPa, a volume of 10.0 L, and a temperature of 720 K. The gas expands isothermally to point B and then expands adiabatically to point C, where its volume is 24.0 L. An isothermal compression brings it to point D, where its volume is 15.0 L. An adiabatic process returns the gas to point A. (a) Determine all the unknown pressures, volumes, and temperatures as you f ill in the following table: (b) Find the energy added by heat, the work done by the engine, and the change in internal energy for each of the steps A B, B C, C D, and D A (c) Calculate the efficiency Wnet/|Qk|. (d) Show that the efficiency is equal to 1 - TC/TA, the Carnot efficiency.

Consider a transformation from point A to B in a two-step process. First, the pressure is lowered from 3 MPa at point A to a pressure of 1 MPa, while keeping the volume at 2 L by cooling the system. The state reached is labeled C. Then the system is heated at a constant pressure to reach a volume of 6 L in the state B. (a) Find the amount of work on the ACB path. (b) Find the amount of heat exchanged by the system when it goes from A to B on the ACB path. (c) the change in the internal energy when the AB process occurs adiabatically with the AB change though the two-step process on the ACB path.

An amount of n moles of a monatomic ideal gas in a conducting container with a movable piston is placed in a large thermal heat bath at temperature T1 and the gas is allowed to come to equilibrium. After the equilibrium is leached, the pressure on the piston is lowered so that the gas expands at constant temperature. The process is continued quasi-statically until the final pressure is 4/3 of the initial pressure p1 . (a) Find the change in the internal energy of the gas. (b) Find the work done by the gas. (c) Find the heat exchanged by the gas, and indicate, whether the gas takes in or gives up heat.