Question

Entropy. Suppose the heat capacity of some system has the form $C_v = aT + bT^3$ for temperatures from zero up to some temperature of interest. Calculate its entropy at temperature T. Under what conditions is your result valid? Suppose there is a phase change at some temperature less than T, and, like the melting of water, that phase change requires some input of heat. Discuss how that would change your approach to finding the entropy. You might use, $C_v = T \left(\frac{\partial S}{\partial T}\right)_{V, N}$ $S(U, V, N) = N k_B \left\{ \ln \left[ \frac{V}{N} \left( \frac{4 \pi m U}{3 h^2 N} \right)^{3/2} \right] + \frac{5}{2} \right\}$

          Entropy. Suppose the heat capacity of some system has the form
$C_v = aT + bT^3$
for temperatures from zero up to some temperature of interest.
Calculate its entropy at temperature T. Under what conditions is your result valid?
Suppose there is a phase change at some temperature less than T, and, like the melting of
water, that phase change requires some input of heat. Discuss how that would change your approach
to finding the entropy.
You might use,
$C_v = T \left(\frac{\partial S}{\partial T}\right)_{V, N}$
$S(U, V, N) = N k_B \left\{ \ln \left[ \frac{V}{N} \left( \frac{4 \pi m U}{3 h^2 N} \right)^{3/2} \right] + \frac{5}{2} \right\}$

$Entropy. Suppose the heat capacity of some system has the form Cv = aT + bT^3 for temperatures from zero up to some temperature of interest. Calculate its entropy at temperature T. Under what conditions is your result valid? Suppose there is a phase change at some temperature less than T, and, like the melting of water, that phase change requires some input of heat. Discuss how that would change your approach to finding the entropy. You might use, Cv = T ((∂ S)/(∂ T))V, N S(U, V, N) = N kB {ln[ (V)/(N)( (4 π m U)/(3 h^2 N))^3/2] + (5)/(2)}$

Added by Daniel K.

Question

Please give Ace some feedback