Suppose that 141 moles of a monatomic ideal gas is initially contained in a pist

Question

Suppose that 141 moles of a monatomic ideal gas is initially contained in a piston with a volume of 1.46 m^3 at a temperature of 362 K. The piston is connected to a hot reservoir with a temperature of 1083 K and a cold reservoir with a temperature of 362 K. The gas undergoes a quasi-static Stirling cycle with the following steps: The temperature of the gas is increased to 1083 K while maintaining a constant volume. The volume of the gas is increased to 4.43 m^3 while maintaining a constant temperature. The temperature of the gas is decreased to 362 K while maintaining a constant volume. The volume of the gas is decreased to 1.46 m^3 while maintaining a constant temperature. It may help you to recall that Cv = 12.47 J/K/mole for a monatomic ideal gas. and that the number of gas molecules is equal to Avagadros number (6.022 times 10^23) times the number of moles of the gas. What is the pressure of the gas under its initial conditions? Pa How much energy is transferred in

Explanation / Answer

1. What is the pressure of the gas under its initial conditions?

Using the ideal gas equation in order to solve for the pressure of the system

Ideal Gas Law Equation:
Pressure * Volume = number of moles * R constant * Temperature
Pressure = (number of moles * R constant * Temperature) / Volume
= ___________Pa

2. How much energy is transferred into the gas from the hot reservoir?
Step 1:
Changes the temperature of the system to 1212K and maintains volume

so we can use the equation for heatEnergy:
heatEnergy =specific heat constant of volume * number of moles * change in temperature

Step 2:

Volume of the system increases, however the temperature of the system remains constant.

Work added into the system is defined by:

Work =number of moles * R Constant * Temperature * ln(Volume Final/Volume Initial)
Add both the heat energy and work that were in the system to obtain the value:
=> _________!

3. How much energy is transferred out of the gas into the cold reservoir?
Step 3:
Changes temperature to 459 K with a constant volume, so we can use step 1's equation to get:

heatEnergy = specific heat constant of volume * number of moles * change in temperature

Step 4:
Volume of the system increases, however the temperature of the system remains constant.
Work added into the system is defined by:
Work = number of moles * R Constant * Temperature * ln(Volume Final/Volume Initial)
Add both energy and work that go into the cold reservoir to get:
= _______ !
4. How much work is done by the gas during this cycle?

Find the difference in heat in and heat out
Work Done By Ga = heat entered - heat exited
= __________ J

5. What is the efficiency of this Stirling cycle?

Efficiency is defined as work done divided by the heat in, which is:

Efficiency Ratio = Work Done by Gas / heatEnergyAdded
= _____________
6. What is the maximum (Carnot) efficiency of a heat engine running between these two reservoirs?

Carnot Efficiency of a heat engine is defined by:

Carnot Efficiency = 1 - (Temperature of Cold Reservoir / Temperature of Hot Reservoir)
= _______________

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