Work done in Adiabatic, Quasistatic-compression

In summary, the homework statement states that to find the work done in an adiabatic, quasistatic compression, one must use (delta)U = Q + W. However, one can also find the work done by using W = -(delta)P*V.
  • #1
Trenthan
54
0

Homework Statement


i have to find the W done in an Adiabatic, Quasistatic compression and I am not having much luck.

Ive calculated it using (delta)U = Q + W, since Q = 0, hence W = change in internal energy

However i want to calculate it using W = -(delta)P*V

The Attempt at a Solution



My working is attached, my text just says to use W = delta(U), but i know there is a way to do it via pressure and volume, I am just not sure where to go from where I am at.

Attempt is attached

Untitled-Scanned-03.jpg


Has to be in terms of TA, n (moles) and R

Cheers Trent
 
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  • #2
I assume we are talking about perfect gases so that indeed [tex]p V^\gamma = const [/tex] for a quasistatic, adiabatic process :p

[tex]

-\int_{V_C}^{V_A} p dV =

\left\{ p V^\gamma = const \right\}=

-\int_{V_C}^{V_A} const \cdot \frac{dV}{V^\gamma}

[/tex]

Determine [tex] const [/tex] from the conditions at A.
 
  • #3
BobbyBear said:
I assume we are talking about perfect gases so that indeed [tex]p V^\gamma = const [/tex] for a quasistatic, adiabatic process :p

[tex]

-\int_{V_C}^{V_A} p dV =

\left\{ p V^\gamma = const \right\}=

-\int_{V_C}^{V_A} const \cdot \frac{dV}{V^\gamma}

[/tex]

Determine [tex] const [/tex] from the conditions at A.

I got it finally thanks heeps but i got it using conditions at "c" our starting point, (PCVCgamma = PVgamma, rearranged for P = and solved from ther) not "A", I am assuming u meant "c"?

Thanks :)
 
  • #4
Oopsie, yes I meant "C" , it's the point where you know P and V to start with. Sorry, I always think that A comes before C when I'm not thinking :P:P

Though now that you said, . . . it's also true that you know P and V of point A too, so you could use any:) of course, they've given you two points such that :
[tex]


p V^\gamma = const1


[/tex]
and
[tex]


T V^{\gamma-1}= const2


[/tex]
with
[tex]


\gamma=5/2


[/tex]
because if this was not so it wouldn't be a reversible, adiabatic process.
 
  • #5
thanks and good point, just trierd it the other way and it works :)
 

1. What is adiabatic compression?

Adiabatic compression refers to a process where the volume of a gas is reduced, resulting in an increase in pressure and temperature, without any heat exchange with the surroundings. This is achieved by insulating the system so that there is no transfer of heat energy.

2. How is work done in adiabatic compression?

In an adiabatic process, work is done by the gas on its surroundings as it expands or compresses. When a gas is compressed adiabatically, the energy used to compress the gas is converted into an increase in temperature and pressure.

3. What is the difference between adiabatic and isothermal compression?

In adiabatic compression, there is no heat exchange with the surroundings, resulting in an increase in temperature. In contrast, isothermal compression occurs at a constant temperature, and any energy input is used to do work on the gas rather than increasing its temperature.

4. What is quasistatic compression?

Quasistatic compression is a process in which the gas is compressed slowly and gradually, allowing it to reach thermal equilibrium with its surroundings at each stage of compression. This ensures that the process is reversible and that the system remains in a state of thermodynamic equilibrium.

5. How is adiabatic compression used in practical applications?

Adiabatic compression is used in various industrial and scientific applications, such as in refrigeration systems, gas turbines, and internal combustion engines. It is also used in laboratory experiments to study the behavior of gases under different conditions.

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