Thermodynamics, Isothermal Question

In summary, the conversation discusses a problem where 10 moles of an ideal gas undergo a reversible change of state along a straight line path on a P-V diagram, with an initial state of P1 = 10 atm and T1 = 300K. The question is how much work is done during the cycle. The solution is found using the equation w = nRT ln(Pi/Pf) and the correct answer is 123.4 kJ. The process is not considered isothermal because the temperature is not constant throughout the whole process. The graphical interpretation of the problem helps in finding the correct answer.
  • #1
kalbuskj31
16
0

Homework Statement



10 moles of an ideal gas, in the initial state P1 = 10 atm, T1 = 300K are taken around the following cycle.

a) A reversible change of state along a straight line path on the P-V diagram to the state P = 1 atm T = 300K. How much work is done during the cycle?

Homework Equations



Isothermal, ΔU = 0 so w = p dV

The Attempt at a Solution



w = p dV and p = nRT/V so w = nRT (dV/V)

w = nRT ln(Vf/Vi) = nRT ln(Pi/Pf)

w = [(10 moles)* (8.3144 J/ K *mole) * (300K)] ln(10atm/1atm)

w = 57.4 kJ but the correct answer is 123.4kJ. Suggestions??
 
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  • #2
The process is not isothermal. You are not taking into account that the graph is a straight line.

You are finding the area under the isothermal curve between the beginning and ending points (PV = constant).

AM
 
  • #3
Andrew Mason said:
The process is not isothermal. You are not taking into account that the graph is a straight line.

You are finding the area under the isothermal curve between the beginning and ending points (PV = constant).

AM

Thanks. Can you please explain why this process isn't considered isothermal?
 
  • #4
kalbuskj31 said:
Thanks. Can you please explain why this process isn't considered isothermal?

An isotherm has the same temperature during the whole process, not just at the start and end points. It will look like an exponential curve on the PV diagram. Adiabats will be "steeper" because they cross the isotherms.

Since it's a straight line, did you try a graphical integration?
 
  • #5
Thank you for the help. the graphical interpretation helped give me the correct answer. I've been out of school for 3 years, so I'm brushing up on everything.
 

1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationships between heat, work, energy, and temperature. It studies how these quantities affect and change the physical properties of matter.

2. What is an isothermal process?

An isothermal process is a thermodynamic process in which the temperature of a system remains constant throughout. This means that the system neither gains nor loses heat during the process.

3. What is the first law of thermodynamics?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy can neither be created nor destroyed; it can only be transferred or converted from one form to another.

4. What is the significance of an isothermal process?

An isothermal process is significant because it allows for the study of the relationship between heat, work, and energy without the complication of temperature changes. This simplifies calculations and allows for a better understanding of the behavior of gases and other substances.

5. What is an ideal gas in an isothermal process?

An ideal gas in an isothermal process follows the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature. In an isothermal process, the temperature remains constant, so the equation simplifies to PV = constant.

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