Question

In: Physics

An ideal gas undergoes the following Carnot Cycle. It starts in a chamber of volume .0065...

An ideal gas undergoes the following Carnot Cycle. It starts in a chamber of volume .0065 m3 and temperature 345 Kelvin and pressure 630 kPa (state 1). It is allowed to expand isothermally to a volume of .01066 m3 (state 2) while heat is added to the gas.  Then it expands adiabatically to a volume of .01784 m3 (state 3). Then, it is compressed isothermally to a volume of Vf m3 (state 4) while heat is extracted from the gas.  Finally, it returns to its initial state in an adiabatic process.  (The gamma of the gas, γ = 1.28,  Cv = 3.5R).

How much heat is added in the 1st isothermal process and the efficiency of this engine?

a.)1.878 kJ, 11.2%

b.) 2.029 kJ, 11.2%

c.) 2.029 kJ, 13.6%

d.) 2.334 kJ, 13.6%

e.) 2.334 kJ, 15.8%

Solutions

Expert Solution

Carnot cycle contains two isothermal(1-2 & 3-4) and two adiabatic(2-3 & 4-1)process.


Related Solutions

Suppose 0.2 moles of an ideal diatomic gas (Cv = 20.8 J/mol·K) undergoes a Carnot cycle...
Suppose 0.2 moles of an ideal diatomic gas (Cv = 20.8 J/mol·K) undergoes a Carnot cycle between temperatures of 227˚C and 27˚C. The initial volume of the gas is 8.31×10-4 m3 and during the high temperature isothermal expansion, the volume doubles.        a) Find the work done during the entire cycle       b) Find the efficiency of the cycle
A mole of an ideal gas goes through a cycle of a Carnot engine. Draw the...
A mole of an ideal gas goes through a cycle of a Carnot engine. Draw the pressure vs volume and entropy vs temperature planes for this cycle. What do the diagrams look like when the efficiency of the cycle is 50% and 99%. Then Calculate the work done per cycle by the gas and find the efficiency of the cycle.
11. Consider a Carnot cycle with 2.25 moles of a diatomic ideal gas as the working...
11. Consider a Carnot cycle with 2.25 moles of a diatomic ideal gas as the working substance (assume Cv = 2.5*R). The following are the steps of the cycle: Step I: reversible, isothermal expansion at 300.0 °C from 10.00 L to 16.00 L. Step II: reversible, a diabatic expansion until the temperature decreases to 50.0 °C. Step III: reversible, isothermal compression at 50.0 °C. Step IV: reversible, adiabatic compression back to the initial conditions. A. Calculate q, w, ΔU, ΔH,...
Analyze Carnot Cycle for ideal gases
Analyze Carnot Cycle for ideal gases
An ideal gas with f = 3 degrees of freedom starts with a volume of 6...
An ideal gas with f = 3 degrees of freedom starts with a volume of 6 liters, a pressure of 1.1×10^5 Pa and a temperature of 20◦C. The gas is compressed adiabatically to 2 liters, then expands at constant temperature back to 6 liters. Then it is again adiabatically compressed to 2 liters, and isothermally expands to 6 liters. Draw the 4 steps in a P −V diagram. Calculate the final pressure and final temperature.
An ideal gas is contained in a piston-cylinder device and undergoes a power cycle as follows:...
An ideal gas is contained in a piston-cylinder device and undergoes a power cycle as follows: 1-2 isentropic compression from an initial temperature T1 5 208C with a compression ratio r 5 5 2-3 constant pressure heat addition 3-1 constant volume heat rejection The gas has constant specific heats with cv 5 0.7 kJ/kg·K and R 5 0.3 kJ/kg·K. (a) Sketch the P-v and T-s diagrams for the cycle. (b) Determine the heat and work interactions for each pro- cess,...
Starting from volume VA and pressure PA, an ideal gas undergoes the following three-stage, reversible, cyclic...
Starting from volume VA and pressure PA, an ideal gas undergoes the following three-stage, reversible, cyclic process: (i) adiabatic expansion to volume VB, then (ii) isochoric heating to pressure PA, then (iii) isobaric cooling to volume VA. Draw this process on a P V -diagram, and evaluate the change in the entropy of the system (∆S), for each stage. Show that the sum of these entropy changes is zero, as it should be since the system returns to its initial...
Carnot cycle is called the ideal cycle. What is the process that is impossible in reality...
Carnot cycle is called the ideal cycle. What is the process that is impossible in reality in the Carnot cycle (among isothermal expansion, insulation expansion, isothermal compression, and insulation compression)?
A monatomic ideal gas (n moles) undergoes this cycle: (1) starting at V1, T1, it increases...
A monatomic ideal gas (n moles) undergoes this cycle: (1) starting at V1, T1, it increases the temperature at constant volume to 3T1; (2) from V1, 3T1, it increases the volume at constant temperature to 2V1; (3) from 2V1, 3T1, it decreases the temperature at constant volume back to the original temperature, T1; (4) from 2V1, T1, it decreases the volume back to the original volume, V1. (a) Sketch the cycle on a P-V diagram. (b) In terms of n...
Calculate each of the following quantities for an ideal gas. a. Calculate the volume of the...
Calculate each of the following quantities for an ideal gas. a. Calculate the volume of the gas, in liters, if 1.35 mol has a pressure of 0.995 atm at a temperature of -6 ∘C. b. Calculate the absolute temperature of the gas at which 3.23×10−3 moloccupies 350. mL at 760. torr. c. Calculate the pressure, in atmospheres, if 4.66×10−2 moloccupies 412 mL at 135 ∘C d. Calculate the quantity of gas, in moles, if 54.7 L at 55.0 ∘C has...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT