91Ó°ÊÓ

Residual molar entropy is given by the expression (a) \(S=R \ln W\) (b) \(S=N \ln W\) (c) \(S=\frac{R}{N} \ln W\) (d) \(S=n R \ln W\)

The Boltzmann entropy equation is (a) \(S=\frac{K}{\ln W}\) (b) \(S=K^{r} \ln \frac{P_{2}}{P_{\mathrm{J}}}\) (c) \(S=K^{\prime} \ln \frac{V_{\mathrm{J}}}{V_{2}}\) (d) \(S=K^{\prime \prime} \ln W\)

The third law of thermodynamics may be stated as follows: (a) At absolute zero the entropy of all perfectly crystalline solids tends to decrease. (b) The entropy of a perfectly crystalline solid may be taken as zero at absolute zero. (c) The entropy of every substance is zero at \(0 \mathrm{~K}\). (d) The entropy of a substance is related to its heat capacity.

From the third law, the entropy of a substance at temperature \(T\) is given as, (a) \(S_{T}=\frac{1}{3} C_{P}\left(\right.\) at \(\left.T_{1}\right)+\int_{T_{1}}^{T} \frac{C_{p}}{T} d T\) (b) \(S=C_{p}\left(\right.\) at \(\left.T_{1}\right)+\int_{\tau_{1}}^{T} C_{p} \ln d T\) (c) \(S=C_{p} \ln T+\int_{\tau_{1}}^{T} \frac{C_{p}}{T} d T\) (d) none of the above

The Nernst heat theorem can be mathematically stated as (a) \(\lim _{T \rightarrow 0} \frac{d(\Delta G)}{d T}=\lim _{T \rightarrow 0} \frac{d(\Delta H)}{d T}=0\) (b) \(\lim _{T \rightarrow 0} \frac{d(\Delta H)}{d T}=\lim _{T \rightarrow 0} \frac{d(\Delta S)}{d T}=0\) (c) \(\lim _{T \rightarrow 0} \frac{d(\Delta V)}{d T}=\lim _{T \rightarrow 0} \frac{d(\Delta A)}{d T}=0\) (d) \(\lim _{r \rightarrow 0} \frac{d(\Delta A)}{d T}-\lim _{r \rightarrow 0} \frac{d(\Delta H)}{d T}\)