Pressure and temperature changes adiabatically for an ideal gas?

[erik-the-red]

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 $$P_i \cdot V_i = P_f \cdot V_f$$. 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.

 

[mezarashi]

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.

$$PV^\gamma = constant$$

Being monoatomic, the values for Cv and Cp are $$C_v = \frac{3}{2}R, C_p = C_v + R$$, which allows you to find gamma, as $$\gamma = \frac{C_p}{C_v}$$.

 

[Chi Meson]

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 $$P_i \cdot V_i = P_f \cdot V_f$$. 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 $$P_i \cdot V_i = P_f \cdot V_f$$ is because the temperature does not remain constant.

 

[erik-the-red]

Thanks mezarashi, that is what I needed.

Chi Meson, thanks for reminding me that temperature is not constant.

 

[Sapphi]

Can someone explain this further? I don't understand what to use for gamma

 

[JazzFusion]

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.