Answer: Solving Three Step Gas Cycle Homework Problem

  • Thread starter Thread starter xmonsterx
  • Start date Start date
  • Tags Tags
    Cycle Gas
AI Thread Summary
The discussion revolves around solving a three-step gas cycle problem involving a monatomic ideal gas. In the first step, the heat added to the gas during constant volume heating needs to be expressed in terms of pressure, volume, and a constant A. The second step requires calculating the work done by the gas during isothermal expansion, while the third step focuses on the work done during isobaric cooling. Participants express confusion over the calculations and seek clarification on how to properly account for initial and final states in their equations. The thread highlights the complexities of thermodynamic processes and the need for accurate application of relevant equations.
xmonsterx
Messages
11
Reaction score
0

Homework Statement


A monatomic ideal gas has pressure p_1 and temperature T_1. It is contained in a cylinder of volume V_1 with a movable piston, so that it can do work on the outside world.

Consider the following three-step transformation of the gas:

1. The gas is heated at constant volume until the pressure reaches Ap_1 (where A >1).
2. The gas is then expanded at constant temperature until the pressure returns to p_1.
3. The gas is then cooled at constant pressure until the volume has returned to V_1.

It may be helpful to sketch this process on the pV plane.

Part 1-
How much heat DeltaQ_1 is added to the gas during step 1 of the process?
Express the heat added in terms of p_1, V_1, and A.

Part 2-
How much work W_2 is done by the gas during step 2?
Express the work done in terms of p_1, V_1, and A.

Part 3-
How much work W_3 is done by the gas during step 3?
If you've drawn a graph of the process, you won't need to calculate an integral to answer this question.
Express the work done in terms of p_1, V_1, and A.

Homework Equations



R = 8.31

The Attempt at a Solution



Part 1-
I tried Q = p_1*V_1*(C_V/R) = 1.5*Ap_1*V_1 but I was told this is the final internal energy, not the change in internal energy. so I worked out that

Q = [1.5*p_1*V_1*(AT_1-T_1)] / T_1 but the answer does not depend on AT_1 or T_1

Part 2-
all I've got so far is
W = nRT*ln(V_f/V_i) = pV*ln(V_f/V_i)
but that's about as far as I get.

Part 3-
I got Ap_1*V_1 but this is what the value would be if it were coming from V = 0. So I re-arranged pV=nRT to eventually get

W = p_1[(p_1V_1)/(Ap_1) - V_1]
but this is also wrong how do I take into account the initial state, wouldn't I just be able to write W = (Ap_1V_1) - V_1 ?
 
Last edited:
Physics news on Phys.org
xmonsterx said:
Consider the following three-step transformation of the gas:

1. The gas is then expanded at constant temperature until the pressure returns to p_1.
2. The gas is then cooled at constant pressure until the volume has returned to V_1.

I think the first step isn't mentioned.
 
Gear300 said:
I think the first step isn't mentioned.

thanks for point that out! i fixed it! now its a three step cycle.

But i still don't know how to figure this problem out!


please help anyone! pleaseeeeeeeeee!
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is（Figure 2）： F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Closed cycle of an ideal gas
Replies
3
Views
1K
Efficiency of a Simple 3-Stage Ideal Gas Cycle: Analyzing Thermal Efficiency η
Replies
3
Views
2K
Finding Heat and Work in a Three-Step Gas Cycle
Replies
4
Views
47K
Energy of a Gas in equilibrium with BB-radiation
Replies
9
Views
2K
Efficiency of Stirling Cycle - Is it the same as the Carnot Engine?
Replies
14
Views
1K
Work done on container receiving gas from high pressure container
Replies
1
Views
1K
Isothermal Compression of a Ideal Gas and Distance
Replies
8
Views
5K
Calculate the work (Thermodynamics)
Replies
11
Views
1K
Chemistry To determine variables in adiabatic reversible process do we need to look up heat capacity?
Replies
1
Views
2K
How Do You Solve Adiabatic Expansion Problems in Thermodynamics?
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top