An ideal gas initially at 4.00atm and 350 k is permitted
toexpand adibatically to 1.50 times its initial volume. findthe
final pressure and temperature if the gas is a)monoatomic;
b)diatomic with cv=.

Explanation:

It is given that initially pressure of ideal gas is 4.00 atm and its temperature is 350 K. Let us assume that the final pressure is and final temperature is .

(a)   We know that for a monoatomic gas, value of is \frac{5}{3}[/tex].

And, in case of adiabatic process,

                = constant              

also,         PV = nRT

So, here     = 350 K,    ,  and  

Hence,      

          = 267 K

Also,   = 4.0 atm,   ,  and  

            = 2.04 atm

Hence, for monoatomic gas final pressure is 2.04 atm and final temperature is 267 K.

(b) For diatomic gas, value of is \frac{7}{5}[/tex].

As,         = constant              

also,         PV = nRT

= 350 K,    ,  and  

          = 289 K

And,   = 4.0 atm,   ,  and  

            = 2.27 atm

Hence, for diatomic gas final pressure is 2.27 atm and final temperature is 289 K.

3. dark matter

empty space could also be a simple vacuum