Isothermal Process Homework: Calculate Q(in) & Q(out)

In summary, the student is trying to find an equation to solve for nRT ln (Va/Vc) when Va and Vc are unknown, but they know that the process is isothermal. They can find the value of nRT by using the ideal gas law and solving for P and V.
  • #1
aznmaverick
12
0

Homework Statement


Calculate Q(in) and Q(out).


Homework Equations


Specific Heat: Cv = 5/2 R
R = 8.314 J/mol K


The Attempt at a Solution


For the process C-> A, it is an isothermic process but we are not given temperature. The equation to finding the total work done from C->A is nRT ln (Va/Vc). How do I get T in order to solve for nRT ln (Va/Vc)?
 

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  • #2
aznmaverick said:
How do I get T in order to solve for nRT ln (Va/Vc)?

Hint: is there a constitutive equation for this substance?
 
  • #3
Mapes said:
Hint: is there a constitutive equation for this substance?

Yes, I got that from Q (from C to A) = Delta U (C to A) + W (C to A) and since Delta U (C to A) = 0, Q (C to A) = W ( C to A).
W (C to A) for an isothermal process is = (Integral from C to A) P dv

Using the formula PV = nRT and solving for P, we get P = nrT/V, so W (C to A) = (Integral from C to A) nRT/V dv, which comes out to be nRT ln v (from C to A). Finally plugging in C and A, we get nRT ln (Va - Vc) = nRT ln (Va/Vc)
 
  • #4
The value of [itex]nRT[/itex] can be easily calculated even though neither n nor T are known. Know what I mean?
 
  • #5
Yes, well, n=1 mole, and T is unknown, but we know that its a constant. So we cannot solve for it?
 
  • #6
How do you know that there's one mole present? Is there more information in the problem statement that you didn't post?

In any case, the ideal gas law connects all these variables together.
 
  • #7
Mapes said:
How do you know that there's one mole present? Is there more information in the problem statement that you didn't post?

In any case, the ideal gas law connects all these variables together.

Yea, 1 mole was a given. T is still not given. So does that mean there's no 'real answer' to this question w/o T given?
 
  • #8
If P, V, and n are known for an ideal gas, then T is known.
 
  • #9
Mapes said:
If P, V, and n are known for an ideal gas, then T is known.

Got it, thanks!
 

Related to Isothermal Process Homework: Calculate Q(in) & Q(out)

1. What is an isothermal process?

An isothermal process is a thermodynamic process in which the temperature remains constant throughout. This means that there is no change in the internal energy of the system.

2. How do you calculate Q(in) and Q(out) for an isothermal process?

Q(in) and Q(out) refer to the heat energy entering and leaving a system during an isothermal process. To calculate these values, you can use the equation Q = nRTln(V2/V1), where n is the number of moles, R is the gas constant, T is the temperature in Kelvin, and V2 and V1 are the final and initial volumes of the system, respectively.

3. What is the significance of an isothermal process?

An isothermal process is important because it allows for the transfer of heat energy without any change in temperature, which can be useful in certain industrial and scientific applications. It also occurs in many natural processes, such as the expansion of a gas in a balloon.

4. Is an isothermal process reversible?

Yes, an isothermal process can be reversible. This means that the process can be reversed without any change in the surroundings or the system. In other words, the system can be returned to its original state without any net change in the system or in the surroundings.

5. How does an isothermal process differ from an adiabatic process?

An isothermal process is one in which the temperature remains constant, while an adiabatic process is one in which there is no heat exchange between the system and its surroundings. In an isothermal process, the internal energy of the system remains constant, while in an adiabatic process, the internal energy may change due to work being done on or by the system.

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