Two pounds of carbon dioxide (CO₂) as an ideal gas executes a Carnot power cycle while operating between thermal reservoirs at 570 and 100°F. The pressures at the initial and final states of the isothermal expansion are 400 and 200 lb/in², respectively. The specific heat ratio is k = 1.24. Determine the thermal efficiency, the work for the isothermal expansion, in Btu, and the work for the adiabatic expansion, in Btu.

Two pounds of carbon dioxide (CO₂) as an ideal gas executes a Carnot power cycle while operating between thermal reservoirs at 570 and 100°F. The pressures at the initial and final states of the isothermal expansion are 400 and 200 lb/in², respectively. The specific heat ratio is k = 1.24. Determine the thermal efficiency, the work for the isothermal expansion, in Btu, and the work for the adiabatic expansion, in Btu.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter3: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 92AP: Two moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a...

See similar textbooks

Similar questions

Two moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with a pressure of 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state. (c) Find work done by the gas in the process. (d) Find the change in internal energy in the process. Assume Cv=5R and Cp=Cv+R for the diatomic ideal gas in the conditions given.
A copper rod of cross-sectional area 5.0 cm2 and length 5.0 m conducts heat from a heat reservoir at 373 K to one at 273 K. What is the time rate of change of the universe's entropy for this process?
A Carnot engine employs 1.5 mol of nitrogen gas as a working substance, which is considered as an ideal diatomic gas with =7.5 at the working temperatures of the engine. The Carnot cycle goes in the cycle ABCDA with AB being an isothermal expansion. The volume at points A and C of the cycle are 5.0103 m3 and 0.15 L, respectively. The engine operates between two thermal baths of temperature 500 K 300 K. (a) Find the values of volume at B and D. (b) How much heat is absorbed by the gas in the AB isothermal expansion? (c) How much work is done by the gas in the AB isothermal expansion? (d) How much heat is given up by the gas in the CD isothermal expansion? (e) How much work is done by the gas in the CD isothermal compression? (f) How much work is done by the gas in the BC adiabatic expansion? (g) How much work is done by the gas in the DA adiabatic compression? (h) Find the value of efficiency of the engine based on the net and heat input. Compare this value to the efficiency of a Carnot engine based on the temperatures of the baths.
In an adiabatic process, oxygen gas in a container is compressed along a path that can be described by the following pressure in atm as a function of volume V, with V0=1L:P=(3.0atm)(V/V)1.2 . The initial and final volumes during the process were 2 L and 1.5 L, respectively. Find the amount of work done on the gas.
Consider a monatomic ideal gas operating through the Carnot cycle. The initial volume of the gas is V1 = 130 × 10-3 m3. What types of processes are going on for each step in this process? During the isothermal compression step, the volume of gas is reduced by a factor of 4. In the adiabatic heating step, the temperature of the gas is doubled. What is the volume at point 3, in cubic meters?
Steam enters an adiabatic turbine steadily at 7 MPa,500C, and 45 m/s, and leaves at 100 kPa and 75 m/s. Ifthe power output of the turbine is 5 MW and the isentropicefficiency is 77 percent, determine (a) the mass flow rateof steam through the turbine, (b) the temperature at the turbineexit, and (c) the rate of entropy generation during thisprocess.
In a very mild winter climate, a heat pump has heat transfer from an environment at 5.00C to one at 35.0C. What is the best possible coefficient of performance for these temperatures? Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics.
During the compression stroke of a certain gasoline engine, the pressure increases from 1.00 atm to 20.0 atm. If the process is adiabatic and the air–fuel mixture behaves as a diatomic ideal gas, (a) by what factor does the volume change and (b) by what factor does the temperature change? Assuming the compression starts with 0.016 0 mol of gas at 27.0°C, find the values of (c) Q, (d) ΔEint, and (e) W that characterize the process.
In an isothermal process, one mole of an ideal monatomic gas at a temperature T is taken from an initial pressure P to a final pressure P/3. Using the convention that work is positive when it is done on the system, what is the work done during the process in terms of R and T?
Repeat the preceding calculations for an ideal diatomic gas expanding adiabatically from an initial volume of 0.500 m3 to a final volume of 1.25 m3, starting at a pressure of 1.01 105 Pa. (You must sketch the curve to find the work.) P2 = PaW ≈ J
A highly non-ideal gas has an entropy given by S=aNU/V, where the internal energy, U is a function of T.Find the pressure, the expression for the heat capacity at constant volume, and the chemical potential.
Water within a piston-cylinder assembly, initially at 10 lbf/in 2 ,500 ∘ F , undergoes an internally reversible process to 80lbf/in 2 ,800 ∘ F , during which the temperature varies linearly with specific entropy. For the water, determine the work and heat transfer, each in Btu/lb. Neglect kinetic and potential energy effects.