Suppose that 200 moles of a monatomic ideal gas is initially contained in a pist

Question

Suppose that 200 moles of a monatomic ideal gas is initially contained in a piston with a volume of 0.61 m3 at a temperature of 451 K. The piston is connected to a hot reservoir with a temperature of 1201 K and a cold reservoir with a temperature of 451 K. The gas undergoes a quasi-static Stirling cycle with the following steps:

The temperature of the gas is increased to 1201 K while maintaining a constant volume.

The volume of the gas is increased to 2.73 m3 while maintaining a constant temperature.

The temperature of the gas is decreased to 451 K while maintaining a constant volume.

The volume of the gas is decreased to 0.61 m3 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 × 1023) times the number of moles of the gas.

2)How much energy is transferred into the gas from the hot reservoir?

-the answer is not 1869750; when I entered this number I got "Remember that there are two steps in the Stirling cycle in which energy is provided to the gas."

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? -the answer is not zero

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?

Explanation / Answer

cylce 1: temperature is increased to 1201 K while maintainging a constant volume at 0.61 m^3.

it is an isochoric process.

then no work is done by the system

hence heat added=change in internal energy=(3/2)*number of moles*R*change in temperature=1.5*8.314*200*(1201-451)=1870650 J

cycle 2: volume of the gas is increased to 2.73 m^3 from 0.61 m^3, keeping temperature constant at 1201 K

as there is no change in temperature, hence there is no change in intenral energy

hence energy supplied to the system=work done by the system=number of moles*R*T*ln(final volume/initial volume)

=200*8.314*1201*ln(2.73/0.61)=2992734.236 J

cycle 3:

temperature of the gas is decreased to 451 K while maintaining a constant volume

then work done=0

heat removed from the system=1.5*200*8.314*(1201-451)=1870650 J

cycle 4:

volume of the gas is decreased from 2.73 m^3 to 0.61 m^3 at 451 K

hence heat removed=work done on the gas=200*8.314*451*ln(2.73/0.61)=1123832.757 J

Q2) energy transferred into the gas from hot resorvior=energy added in cycle 1+energy added in cycle 2=1870650+2992734.236=4863384.236 J

Q3. heat transferred out of the gas=heat removed in cycle 3+ heat removed in cycle 4

=1870650+1123832.757=2994482.757 J

Q4) work done by the gas =work done by the gas in cycle 2-work done on the gas in cycle 4=2992734.236-1123832.757=1868901.479 J

Q5)efficiency=work done/heat added=1868901.479/4863384.236=38.428%

Q6. maximum efficiency=1-(cold temperature/hot temperature)=1-(451/1201)=62.447%

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.