Adiabatic Process in a heat engine

In summary, the conversation discusses the use of a diatomic gas in a heat engine and the determination of pressure, volume, temperature, work, heat, and change in energy for various processes. There is a discrepancy in the calculations for point 2 and it is suggested to check the calculation for the number of moles. The equation for the adiabat is also mentioned.
  • #1
talaroue
303
0

Homework Statement


A heat engine uses a diatomic gas that follows the pV cycle shown in Figure.
Part 2→3 is adiabat, part 3→1 is isotherm, V=1040 cm3, P=100 kPa, T1=212 K.

Phys.jpg



Determine the pressure at point 2.

Determine the volume at point 2.

Determine the temperature at point 2.

Find Ws for process 1→2.


Find Q for process 1→2.

Tries 0/9
Find ∆E for process 1→2.

Tries 0/9
Find Ws for process 2→3.

Tries 0/9
Find Q for process 2→3.
0 J

Find ∆E for process 2→3.

Find Ws for process 3→1.

Find Q for process 3→1.

Tries 0/9
Find ∆E for process 3→1.

Tries 0/9
What is the thermal efficiency of this heat engine? (in percent)

Homework Equations





The Attempt at a Solution



phys3-1.jpg



I know how to do the rest if I can find the temperature at point 2. I tried 2 different ways.

1. I tried using the Ideal Gas law PV=nRT and solved for mols at pt 1. Then tried using that for point 2 and then used PV=nRT but that didn't work.

2. Then I tried just simply using PV/T=PV/T and came up with the same answer and they are both wrong.

What am I doing wrong?
 
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  • #2
this would help out a lot!
 
  • #3
WHat is the equation i use to find the Work from point 2 to point 3?
 
  • #4
It looks like there is a typo here. We know pv=constant for an isotherm, yet we have pv=2PV at 1, and pv=PV at 3. I suspect it should be p=0.5P at 3, judging from the scale of the p-axis.

For the adiabat, a useful equation is
pvγ = constant​

(Look up γ[/SUP] for an ideal diatomic gas in your textbook, if you're not sure what it is.)
 
  • #5
I understand what that symbol means for monatomic its 5/3 and for diatomic its 7/5. But for the W for 2-->3 I tried using the following...

W=nCv(delta T)
n-mols Cv-constant volume Delta T- Change in temp.

W=(.118 mol)(5/2)(8.31)(369.1-212)=138
 
  • #6
I get a different number of moles than you did, calculated using p, v, and T at point 1. Perhaps you should reproduce that calculation.

I agree with the 369 K temperature at point 3.
 

1. What is an adiabatic process in a heat engine?

An adiabatic process in a heat engine is a thermodynamic process in which there is no transfer of heat between the system and its surroundings. This means that the system is insulated and cannot exchange heat with its surroundings.

2. What is the significance of an adiabatic process in a heat engine?

Adiabatic processes are important in heat engines because they allow for the efficient conversion of thermal energy into mechanical work. This is because no energy is lost as heat during the process, resulting in a higher efficiency compared to non-adiabatic processes.

3. How does an adiabatic process affect the temperature of a system?

During an adiabatic process, the temperature of a system can change due to the work done on or by the system. If work is done on the system, its temperature will increase, and if work is done by the system, its temperature will decrease. However, the overall change in temperature will be less compared to a non-adiabatic process.

4. What is the mathematical representation of an adiabatic process in a heat engine?

The mathematical representation of an adiabatic process in a heat engine is given by the equation PV^γ = constant, where P is the pressure, V is the volume, and γ is the adiabatic index or heat capacity ratio. This equation describes the relationship between pressure and volume during an adiabatic process.

5. What are some real-life examples of adiabatic processes in heat engines?

Some real-life examples of adiabatic processes in heat engines include the compression and expansion of gases in car engines, the compression and expansion of air in refrigerators and air conditioners, and the compression and expansion of air in gas turbines used for power generation. In all of these processes, no heat is exchanged with the surroundings, making them adiabatic processes.

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