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neibegafig
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Hi, I am hoping someone may be able to help me as i am quite stuck in this question.
Suppose that 156 moles of a monatomic ideal gas is initially contained in a piston with a volume of 0.5 m3 at a temperature of 384 K. The piston is connected to a hot reservoir with a temperature of 1112 K and a cold reservoir with a temperature of 384 K. The gas undergoes a quasi-static Stirling cycle with the following steps:
1.) The temperature of the gas is increased to 1112 K while maintaining a constant volume.
2.) The volume of the gas is increased to 2.5 m3 while maintaining a constant temperature.
3.) The temperature of the gas is decreased to 384 K while maintaining a constant volume.
4.) The volume of the gas is decreased to 0.5 m3 while maintaining a constant temperature.
It may help you to recall that CV = 12.47 J/K/mole for a monatomic ideal gas, Avagadros number (6.022E23) times the number of moles of the gas.
1) What is the pressure of the gas under its initial conditions?
2) How much energy is transferred into the gas from the hot reservoir?
3) How much energy is transferred out of the gas into the cold reservoir?
4) How much work is done by the gas during this cycle?
5) What is the efficiency of this Stirling cycle?
6) What is the maximum (Carnot) efficiency of a heat engine running between these two reservoirs?
for 1, 5, and 6 i Got just fine, 1 was Pi = nNkTi/Vi = 995604.48 Pa, 5 was stirling energy efficiency of ((Th-Tc)/Th) * NkLn5/(NkLn5 + Cv(Th-Tc)/Th) = 0.4065, and 6 was 1 - (Tc/Th) = 0.6546
I have some idea on getting 2,3, and 4 but I am stuck. I know that Q = nk(dT) + W where n is the number of moles, k is 1.381E-23, and dT is change in Temperature, I am stuck though as to what W is exactly and what the formula for it would be in the two situations (2, and 3). Would someone be able to help?
Suppose that 156 moles of a monatomic ideal gas is initially contained in a piston with a volume of 0.5 m3 at a temperature of 384 K. The piston is connected to a hot reservoir with a temperature of 1112 K and a cold reservoir with a temperature of 384 K. The gas undergoes a quasi-static Stirling cycle with the following steps:
1.) The temperature of the gas is increased to 1112 K while maintaining a constant volume.
2.) The volume of the gas is increased to 2.5 m3 while maintaining a constant temperature.
3.) The temperature of the gas is decreased to 384 K while maintaining a constant volume.
4.) The volume of the gas is decreased to 0.5 m3 while maintaining a constant temperature.
It may help you to recall that CV = 12.47 J/K/mole for a monatomic ideal gas, Avagadros number (6.022E23) times the number of moles of the gas.
1) What is the pressure of the gas under its initial conditions?
2) How much energy is transferred into the gas from the hot reservoir?
3) How much energy is transferred out of the gas into the cold reservoir?
4) How much work is done by the gas during this cycle?
5) What is the efficiency of this Stirling cycle?
6) What is the maximum (Carnot) efficiency of a heat engine running between these two reservoirs?
for 1, 5, and 6 i Got just fine, 1 was Pi = nNkTi/Vi = 995604.48 Pa, 5 was stirling energy efficiency of ((Th-Tc)/Th) * NkLn5/(NkLn5 + Cv(Th-Tc)/Th) = 0.4065, and 6 was 1 - (Tc/Th) = 0.6546
I have some idea on getting 2,3, and 4 but I am stuck. I know that Q = nk(dT) + W where n is the number of moles, k is 1.381E-23, and dT is change in Temperature, I am stuck though as to what W is exactly and what the formula for it would be in the two situations (2, and 3). Would someone be able to help?