Ideal gas law and thermodyanimic processes

In summary, the gas expands isothermally from V1 to V2, and the entropic change is given by ΔS=nRln(8.5V1/V1)
  • #1
castrodisastro
82
0

Homework Statement


An ideal gas is enclosed in a cylinder with a movable piston at the top. The walls of the cylinder are insulated, so no heat can enter or exit. The gas initially occupies volume V1 and has pressure p1 and temperature T1. The piston is then moved very rapidly to a volume of V2=8.5V1. The process happens so rapidly that the enclosed gas does not do any work.

Find p2, T2, and the change in entropy of the gas. [Express your answers in terms of p1, T1, n, and R.]


Homework Equations


p1V1=p2V2
pV=nRT
ΔS=nRln(Vf/Vi)

The Attempt at a Solution



To determine p2 I used the relationship p1V1=p2V2

p2=(p1V1)/V2

p2=(p1V1)/(8.5V1)

p2=(p1)/8.5


To determine T2 we see that the process itself is an isothermal process since no work was done, and no heat escaped, Q=W. So the temperature will not have changed.
T2=T1


I can't seem to determine ΔS correctly. Since the process is an isothermal expansion, the change in entropy is given by the equation

ΔS=nRln(V2/V1)

from this I can substitute 8.5V1 for V2, resulting in

ΔS=nRln((8.5)V1/V1)

ΔS=nRln(8.5)

This answer however, is incorrect. The problem asks to put in the answer in terms of p1, T1, n, R. The format of this question is a blank field that allows me to create an equation with subscripts, superscripts, fractions, matrices, etc. FYI.

Any help is appreciated, thanks in advance.
 
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  • #2
Maybe they want you to put a number in for ln(8.50)?
 
  • #3
I tried putting

nR(2.14) but that was also incorrect
 
  • #4
castrodisastro said:
I tried putting

nR(2.14) but that was also incorrect
I don't know what to say. That's the answer I would have obtained. Maybe 2.14nR, as if that could possibly matter.
 
  • #5
I am going to have to email the professor about it then. Thank you
 

FAQ: Ideal gas law and thermodyanimic processes

1. What is the ideal gas law?

The ideal gas law is an equation that describes the relationship between the pressure, volume, temperature, and number of moles of a gas. It is represented by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

2. What are the assumptions of the ideal gas law?

The ideal gas law assumes that the gas particles have negligible volume and do not interact with each other, that the gas particles are in constant, random motion, and that the collisions between the gas particles and the walls of the container are perfectly elastic.

3. How does the ideal gas law relate to thermodynamic processes?

The ideal gas law is used to analyze thermodynamic processes, such as isothermal, adiabatic, and isobaric processes. It helps to determine the changes in pressure, volume, and temperature of a gas during these processes.

4. What is the significance of the gas constant (R) in the ideal gas law?

The gas constant (R) is a proportionality constant that relates the properties of a gas to the amount of the gas present. It has a value of 8.314 J/mol K and is used to convert between different units of pressure, volume, and temperature in the ideal gas law equation.

5. Can the ideal gas law be applied to all gases?

The ideal gas law is most accurate for gases at low pressures and high temperatures, where the gas particles are far apart and the effects of intermolecular forces are minimal. However, it can still be used as an approximation for real gases under other conditions.

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