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`-` 3.2 a)

Ta có: $E_{nt} = bV^{\alpha} \Rightarrow V = \left(\frac{E_{nt}}{b}\right)^{\frac{1}{\alpha}}$ 

$dE_{nt} = \alpha b V^{\alpha - 1} dV \Rightarrow dV = \frac{dE_{nt}}{\alpha b V^{\alpha - 1}}$

$A = \int_{E_{nt1}}^{E_{nt2}} p \frac{dE_{nt}}{\alpha b V^{\alpha - 1}} = \int_{E_{nt1}}^{E_{nt2}} \frac{p}{\alpha b V^{\alpha - 1}} dE_{nt}$ 

Có: 

$p = \frac{nRT}{V} = \frac{nRT}{\left(\frac{E_{nt}}{b}\right)^{\frac{1}{\alpha}}}$

 $A = \int_{E_{nt1}}^{E_{nt2}} \frac{nRT}{\left(\frac{E_{nt}}{b}\right)^{\frac{1}{\alpha}}} \frac{dE_{nt}}{\alpha b V^{\alpha - 1}} = \int_{E_{nt1}}^{E_{nt2}} \frac{nRT}{\alpha b V^{\alpha - 1} \left(\frac{E_{nt}}{b}\right)^{\frac{1}{\alpha}}} dE_{nt}$

 `->` $E_{nt} = bV^{\alpha} \Rightarrow V^{\alpha - 1} = \left(\frac{E_{nt}}{b}\right)^{\frac{\alpha - 1}{\alpha}}$

 $A = \int_{E_{nt1}}^{E_{nt2}} \frac{nRT}{\alpha b \left(\frac{E_{nt}}{b}\right)^{\frac{\alpha - 1}{\alpha}} \left(\frac{E_{nt}}{b}\right)^{\frac{1}{\alpha}}} dE_{nt} = \int_{E_{nt1}}^{E_{nt2}} \frac{nRT}{\alpha b \left(\frac{E_{nt}}{b}\right)} dE_{nt} $

$= \int_{E_{nt1}}^{E_{nt2}} \frac{nRT b}{\alpha b E_{nt}} dE_{nt} = \int_{E_{nt1}}^{E_{nt2}} \frac{nRT}{\alpha E_{nt}} dE_{nt}$ 

$= \frac{nRT}{\alpha} \ln\left(\frac{E_{nt2}}{E_{nt1}}\right)$ 

`-` b)

Có: $Q = \Delta E_{nt} - A = b(V_2^{\alpha} - V_1^{\alpha}) - \frac{nRT}{\alpha} \ln\left(\frac{E_{nt2}}{E_{nt1}}\right) $

`-` Nhiệt dung mol của khí:

$C = \frac{b(V_2^{\alpha} - V_1^{\alpha}) - \frac{nRT}{\alpha} \ln\left(\frac{E_{nt2}}{E_{nt1}}\right)}{n(T_2 - T_1)}$