Please answer it all and correct Suppose that 229 moles of a monatomic ideal gas
ID: 3162547 • Letter: P
Question
Please answer it all and correct
Suppose that 229 moles of a monatomic ideal gas is initially contained in a piston with a volume of 1.18 m^3 at a temperature of 493 K. The piston is connected to a hot reservoir with a temperature of 1258 K and a cold reservoir with a temperature of 493 K. The gas undergoes a quasi-static Stirling cycle with the following steps: The temperature of the gas is increased to 1258 K while maintaining a constant volume. The volume of the gas is increased to 3.87 m^3 while maintaining a constant temperature. The temperature of the gas is decreased to 493 K while maintaining a constant volume. The volume of the gas is decreased to 1.18 m^3 while maintaining a constant temperature. It may help you to recall that C_V = 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? You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. How much energy is transfer into the gas from the hot reservoir? You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. How much energy is transferred out of the gas into the cold reservoir? 2184556.9 You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. How much work is done by the gas during this cycle? You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. What is the efficiency of this Stirling cycle? You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. What is the maximum (Carnot) efficiency of a heat engine running between these two reservoirs?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)
= _______________