Find Work of Isothermal Expansion: Questions Answered

In summary: V_i## and ##V_f## are the initial and final volumes, respectively. There are no subscripts for the initial and final volumes in the equation, but they are specified in the question. The equation does not explicitly state that the gas behaves ideally, but it can be used for ideal gases as well. Knowing the initial volume is necessary to calculate the work. In summary, for a reversible isothermal expansion at a known temperature, the work can be calculated using the given equation of state by integrating pdV and using the initial and final volumes.
  • #1
Pixter
30
0
have a question.
the viral eqn of state for one mole of aragon is:

pV=RT(1+B/V +c/V^2)

T is known and so is B and C. but p is not known.
initial V is known and so is final V.

the question is "find out the work of a reversible isothermal expansion at this temperature"

Know I'm wondering is there something wrong with the eqn. is there suppose to be some subscripts for inital and final on the V? or am i suppose to figure out a way of rearranging or exchanging part of the eqn with other stuff?

can I exchange stuff that would normally describe an ideal gas?.. it doesn't say that it acts ideal and by the first eqn it doesn't seem as it does. so...
if the eqn is correct do i need to know V?

edit: oki if a move the v over to the left and then integrate.. do i get work or do i have to put something else in there... W=integral of pdV

ps: sorry for posting in the wrong forum.. now the homework. but donät know how to delete it.. if someone could please move it or something.. thanx
 
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  • #2
From the specified equation of state, the pressure is given by ##p=RT(1/V+B/V^2 +C/V^3)##. Integrating pdV to get the work then gives $$W=RT\left(\ln{(V_f/V_i)}+B(\frac{1}{V_i}-\frac{1}{V_f})+\frac{C}{2}(\frac{1}{V_i^2}-\frac{1}{V_f^2})\right)$$
 

1. What is isothermal expansion?

Isothermal expansion is a thermodynamic process in which a system undergoes a change in volume while maintaining a constant temperature. This means that the heat added to the system is equal to the work done by the system.

2. How do you calculate the work of isothermal expansion?

The work of isothermal expansion can be calculated using the equation W = nRTln(V2/V1), where W is the work, n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, and V1 and V2 are the initial and final volumes of the gas, respectively.

3. What is the significance of isothermal expansion in thermodynamics?

Isothermal expansion is significant because it allows us to understand the relationship between pressure, volume, and temperature of a gas. It also helps us to calculate the work done by a gas and the heat added to or removed from the system.

4. What are some real-world applications of isothermal expansion?

Isothermal expansion is commonly used in refrigerators and heat engines. It is also used in the production of compressed air and in chemical reactions where gases are involved.

5. How does isothermal expansion differ from adiabatic expansion?

In isothermal expansion, the temperature of the system remains constant, while in adiabatic expansion, there is no heat exchange between the system and its surroundings. This means that in adiabatic expansion, the temperature of the system changes, while in isothermal expansion it does not.

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