$(25\%)$ Q$2.($a$)$ Predict the value for the enthalpy of vaporization for water at $200C$ assuming$(25\%)$ Q$2.($a$)$ Predict the value for the enthalpy of vaporization for water at $200C$ assuming

steam to be an ideal gas. Calculate the percent error.

Hint: $h_{fg}=T_0{v}_{fg}(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}}{)}_v$

$($b$)$ Suppose the steam tables started at $P_{\text{s}\text{a}\text{t}}=2$kPa$(T_{\text{s}\text{a}\text{t}}=17\mathrm{.}5C)$ and we desired $T_{\text{s}\text{a}\text{t}}$ at $P_{\text{s}\text{a}\text{t}}=1$

kPa. Predict $T_{\text{s}\text{a}\text{t}}$ and compare with the value from the steam tables.

Hint: $ln(\frac{P_2}{P_1}{)}_{\text{s}\text{a}\text{t}}$~$=\frac{h_{fg}}{R}(\frac{1}{T_1}-\frac{1}{T_2}{)}_{\text{s}\text{a}\text{t}}$

$($c$)$ Calculate the entropy change of a $10-$kg block of copper if the pressure changes from $100$

kPa to $50$MPa while the temperature remains constant. Use $=5{10}^{-5}{K}^{-1}$ and $=8770$

$k\frac{g}{m^3}.$

Hint: Use Maxwel's equations and $=\frac{1}{v}(\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{T}}{)}_P$

$($d$)$ Find the Joule$-$Thomson coefficient for steam at $400C$ and $1$MPa using both expressions

given in $(11\mathrm{.}63).$

Hint: Use $C_p=T(\frac{\text{d}\text{e}\text{l}\text{s}}{\text{d}\text{e}\text{l}\text{T}}{)}_P$ and ${}_j=(\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{P}}{)}_h=\frac{1}{C_p}[T(\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{T}}{)}_P-v]$

$($e$)$ Verify the Clapeyron equation for R$134$a at $500$kPa.

Hint: $(del\frac{P}{d}$elT${)}_v=\frac{h_{fg}}{T}{v}_{fg}$

steam to be an ideal gas. Calculate the percent error.

Hint: $h_{fg}=T_0{v}_{fg}(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}}{)}_v$

$($b$)$ Suppose the steam tables started at $P_{\text{s}\text{a}\text{t}}=2$kPa$(T_{\text{s}\text{a}\text{t}}=17\mathrm{.}5C)$ and we desired $T_{\text{s}\text{a}\text{t}}$ at $P_{\text{s}\text{a}\text{t}}=1$

kPa. Predict $T_{\text{s}\text{a}\text{t}}$ and compare with the value from the steam tables.

Hint: $ln(\frac{P_2}{P_1}{)}_{\text{s}\text{a}\text{t}}$~$=\frac{h_{fg}}{R}(\frac{1}{T_1}-\frac{1}{T_2}{)}_{\text{s}\text{a}\text{t}}$

$($c$)$ Calculate the entropy change of a $10-$kg block of copper if the pressure changes from $100$

kPa to $50$MPa while the temperature remains constant. Use $=5{10}^{-5}{K}^{-1}$ and $=8770$

$k\frac{g}{m^3}.$

Hint: Use Maxwel's equations and $=\frac{1}{v}(\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{T}}{)}_P$

$($d$)$ Find the Joule$-$Thomson coefficient for steam at $400C$ and $1$MPa using both expressions

given in $(11\mathrm{.}63).$

Hint: Use $C_p=T(\frac{\text{d}\text{e}\text{l}\text{s}}{\text{d}\text{e}\text{l}\text{T}}{)}_P$ and ${}_j=(\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{P}}{)}_h=\frac{1}{C_p}[T(\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{T}}{)}_P-v]$

$($e$)$ Verify the Clapeyron equation for R$134$a at $500$kPa.

Hint: $(del\frac{P}{d}$elT${)}_v=\frac{h_{fg}}{T}{v}_{fg}$