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  • A monatomic ideal gas is confined to move in two dimensions. What is the constant volume specific heat for this gas?
  • Consider a system of N independent harmonic oscillators moving in two dimensions. What is $C_v$ for the system.

For the first case, I guess this one is $C_v = \frac{3}{2}R$. Am I correct? However for the second case, I was confused a little bit. Any help on this?

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Recall the general formula for the specific heat capacity (or check Wikipedia) as a function of the degrees of freedom, then think about how many degrees of freedom an harmonic oscillator has. –  Claudius Dec 7 '12 at 13:51
    
I'm a little bit confused by the formula, though. For the first case, since the gas is forced to move in two dimensions, the degrees of freedom would be 2, right? so $Cv = R * 2/2 = R$? However, wiki said for monatomic gas, $Cv = 1.5R$ –  abcXYZ Dec 7 '12 at 14:03
    
It said this for a monoatomic gas in three dimensions. –  Claudius Dec 7 '12 at 14:06
    
I missed that. So similarly, for the second case $Cv = R * N * 2 / 2 = NR$? –  abcXYZ Dec 7 '12 at 14:14
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