Need help finding spring constant from volume, area, temperature and distance

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SUMMARY

The discussion centers on calculating the final temperature (Tf) of an ideal gas confined in a cylinder with a massless piston attached to an ideal spring. The initial conditions include a volume (V0) of 6.00 x 10^-4 m^3, an area (A) of 2.50 x 10^-3 m^2, and an initial temperature (T0) of 273 K. Participants clarify that the spring constant (k) is not necessary for solving the problem, as it cancels out in the equations. The final temperature can be expressed as Tf = [T0*(V0+A*ΔX)*Xf/A] / [(X0*V0)/A], where ΔX represents the change in spring stretch.

PREREQUISITES
  • Understanding of ideal gas laws and equations.
  • Familiarity with the concepts of pressure, volume, and temperature relationships.
  • Knowledge of spring mechanics and Hooke's Law.
  • Basic algebra for manipulating equations and solving for variables.
NEXT STEPS
  • Learn about the Ideal Gas Law and its applications in thermodynamics.
  • Study the relationship between pressure, volume, and temperature in gas systems.
  • Explore Hooke's Law and its implications in mechanical systems involving springs.
  • Investigate how to derive expressions for thermodynamic variables in ideal gas scenarios.
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This discussion is beneficial for physics students, engineers, and anyone interested in thermodynamics and mechanical systems involving gases and springs.

defmar
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An ideal gas is confined to a cylinder by a massless piston that is attached to an ideal spring. Outside the cylinder is a vacuum. The cross-sectional area of the piston is A = 2.50*10^-3 m^2. The initial pressure, volume, and temperature of the gas are, respectively, P0, V0 = 6.00*10^-4 m^3 and T0 = 273 K, and the spring is initially stretched by an amount x0 = 0.800 m with respect to its unstrained length. The gas is heated, so that its final pressure, volume, and temperature are Pf, Vf and Tf and the spring is stretched by an amount xf = 0.1000 m with respect to its unstrained length. What is the final temperature of the gas?

For the life of me, I cannot find the spring constant k that is needed to solve the rest of the entire problem. I know that KE = (3/2)kT, but I don't know KE either. I'm not given the initial pressure, just the variable. Anyone able to help me find k? I'm lost on how to come up with it.
 
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defmar said:
An ideal gas is confined to a cylinder by a massless piston that is attached to an ideal spring. Outside the cylinder is a vacuum. The cross-sectional area of the piston is A = 2.50*10^-3 m^2. The initial pressure, volume, and temperature of the gas are, respectively, P0, V0 = 6.00*10^-4 m^3 and T0 = 273 K, and the spring is initially stretched by an amount x0 = 0.800 m with respect to its unstrained length.
You can't solve for k or n. But you do not have to find k or n.

Just write the expression for P0 in terms of x0, A, V0, n and T0 and similarly write the expression for Pf . When you solve for Tf you will see that k and n drop out.

AM
 
Andrew Mason said:
You can't solve for k or n. But you do not have to find k or n.

Just write the expression for P0 in terms of x0, A, V0, n and T0 and similarly write the expression for Pf . When you solve for Tf you will see that k and n drop out.

AM

Thank you.

I'm getting T_f = [T_0*(V_0+A*ΔX)*X_f/A] / [(X_0*V_0)/A] solving :)
 
defmar said:
Thank you.

I'm getting T_f = [T_0*(V_0+A*ΔX)*X_f/A] / [(X_0*V_0)/A] solving :)
What is Δx?

What is your expression for P in terms of k, x and A? What is Pf/P0?

What is Pf/P0 in terms of Tf, T0, Vf and V0?

Work out Tf from that.

AM
 

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