Pressure and temperature changes adiabatically for an ideal gas?

  • #1
Question:

An ideal gas, which is initially at a pressure of 4.05 atm and a temperature of 355 K is permitted to expand adiabatically to 1.51 times its initial volume.

A.
Find the final pressure if the gas is monatomic.

I was thinking [tex]P_i \cdot V_i = P_f \cdot V_f[/tex]. But, I made no use of the information that the gas is monatomic. Later on, a question asks for the final pressure if the gas is diatomic. Well, my starting point wouldn't distinguish between the two, so it's not right.
 

Answers and Replies

  • #2
mezarashi
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I would suppose you need to use the law for adiabatic expansion of an ideal gas. Of course, the ideal gas law holds as well.

[tex]PV^\gamma = constant[/tex]

Being monoatomic, the values for Cv and Cp are [tex]C_v = \frac{3}{2}R, C_p = C_v + R[/tex], which allows you to find gamma, as [tex]\gamma = \frac{C_p}{C_v}[/tex].
 
  • #3
Chi Meson
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erik-the-red said:
Question:
An ideal gas, which is initially at a pressure of 4.05 atm and a temperature of 355 K is permitted to expand adiabatically to 1.51 times its initial volume.
A.
Find the final pressure if the gas is monatomic.
I was thinking [tex]P_i \cdot V_i = P_f \cdot V_f[/tex]. But, I made no use of the information that the gas is monatomic. Later on, a question asks for the final pressure if the gas is diatomic. Well, my starting point wouldn't distinguish between the two, so it's not right.
The reason you can't use [tex]P_i \cdot V_i = P_f \cdot V_f[/tex] is becuase the temperature does not remain constant.
 
  • #4
Thanks mezarashi, that is what I needed.

Chi Meson, thanks for reminding me that temperature is not constant.
 
  • #5
1
0
Can someone explain this further? I don't understand what to use for gamma
 
  • #6
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mezarashi had it right - gamma is the ratio of Cp / Cv.

Check your text for Cv of a monatomic ideal gas, and Cv of a diatomic ideal gas, then use the fact that Cp is Cv + R, for an ideal gas.
 

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