Question

Consider a classical ideal gas with equation of state $pV = Nk_BT$ and constant heat capacity $C_V = Nk_Balpha$ for some number $alpha$. Show that $C_p = Nk_B(alpha + 1)$ and that the entropy is $S = Nk_B lnleft(frac{V}{N} ight) + Nk_Balpha ln(T) + const$. Deduce that, for an adiabatic process, $VT^alpha$ is constant and, equivalently $pV^gamma$ is constant, where $gamma = C_p/C_V$. (Hint: use the results from problem 1 on the first assignment.)

          Consider a classical ideal gas with equation of state $pV = Nk_BT$ and constant heat capacity $C_V = Nk_Balpha$ for some number $alpha$. Show that $C_p = Nk_B(alpha + 1)$ and that the entropy is
$S = Nk_B lnleft(frac{V}{N}
ight) + Nk_Balpha ln(T) + const$.
Deduce that, for an adiabatic process, $VT^alpha$ is constant and, equivalently $pV^gamma$ is constant, where $gamma = C_p/C_V$. (Hint: use the results from problem 1 on the first assignment.)

$Consider a classical ideal gas with equation of state pV = NkBT and constant heat capacity CV = NkBalpha for some number alpha. Show that Cp = NkB(alpha + 1) and that the entropy is S = NkB lnleft(fracVN ight) + NkBalpha ln(T) + const. Deduce that, for an adiabatic process, VT^alpha is constant and, equivalently pV^gamma is constant, where gamma = Cp/CV. (Hint: use the results from problem 1 on the first assignment.)$

Added by Brenda G.

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