The difference of specific heats for an ideal gas, (c_{p, m}-c_{v, m}=Re). Evaluate the difference in specific

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The difference of specific heats for an ideal gas, \(c_{p, m}-c_{v, m}=\Re\). Evaluate the difference in specific heats for gases obeying (1) the van der Waals and (2) the Dieterici equations of state. Comment on the results for the difference in specific heat for these gases compared with the ideal gas.

\(\left[\Re /\left(1-\frac{2 a(v-b)^{2}}{\Re T v^{3}}\right)\right]\)

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The expression you provided for the difference in specific heats cp mcv mRe holds true for ideal gases However when dealing with gases obeying different equations of state such as the van der Waals equation or the Dieterici equation the difference in specific heats may not directly equal the gas constant Re For gases obeying the van der Waals equation of state the expression you provided leftRe left1frac2avb2Re Tv3 ight ight represents an approximation for the difference in specific heats It takes into account the deviations from ideality caused by the van der Waals equation This equation considers the attractive forces parameterized by a and the excluded volume parameterized by b of the gas molecules Similarly for gases obeying the Dieterici equation of state there will be a different expression for the difference in specific heats that accounts for the deviations from ideality described by the Dieterici equation In summary while the difference in specific heats for an ideal gas ...View the full answer

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