Problem $4(60$ points$)$: Calculate the required specific property values$($specific volume $V,$specific entropy $S,$ specific internal energy $u,$ specific enthalpy $h,$ quality $x)$ and other property values$($pressure $P$ and temperature $T)$ for both initial state and final state based on the given property information or process characterization. Then calculate the difference of specific internal energy, the difference of specific enthalpy and the difference of specific entropy.

$(1)$ Material of Substance: $H_{2}O$

Initial State: $P_1=10$MPa,$v_1=0\mathrm{.}0031\frac{m^3}{k}g$

Final State: $T_2=200C,v_2=0\mathrm{.}11\frac{m^3}{k}g$

For initial state, determine $T_1=,s_1=,u_1=,h_1=,x_1=?$

For final state, determine $P_2=,s_2=,u_2=,h_2=,x_2=$

For the process change, determine

$s=s_2-s_1=$

$u=u_2-u_1=$

$h=h_2-h_1=$

Problem $4(60$ points$)$: Calculate the required specific property values$($specific volume $V,$specific entropy $S,$ specific internal energy $u,$ specific enthalpy $h,$ quality $x)$ and other property values$($pressure $P$ and temperature $T)$ for both initial state and final state based on the given property information or process characterization. Then calculate the difference of specific internal energy, the difference of specific enthalpy and the difference of specific entropy.

$(1)$ Material of Substance: $H_{2}O$

Initial State: $P_1=10$MPa,$v_1=0\mathrm{.}0031\frac{m^3}{k}g$

Final State: $T_2=200C,v_2=0\mathrm{.}11\frac{m^3}{k}g$

For initial state, determine $T_1=,s_1=,u_1=,h_1=,x_1=?$

For final state, determine $P_2=,s_2=,u_2=,h_2=,x_2=$

For the process change, determine

$s=s_2-s_1=$

$u=u_2-u_1=$

$h=h_2-h_1=$

Problem $4(60$ points$)$: Calculate the required specific property values$($specific volume $V,$specific entropy $S,$ specific internal energy $u,$ specific enthalpy $h,$ quality $x)$ and other property values$($pressure $P$ and temperature $T)$ for both initial state and final state based on the given property information or process characterization. Then calculate the difference of specific internal energy, the difference of specific enthalpy and the difference of specific entropy.

$(1)$ Material of Substance: $H_{2}O$

Initial State: $P_1=10$MPa,$v_1=0\mathrm{.}0031\frac{m^3}{k}g$

Final State: $T_2=200C,v_2=0\mathrm{.}11\frac{m^3}{k}g$

For initial state, determine $T_1=,s_1=,u_1=,h_1=,x_1=?$

For final state, determine $P_2=,s_2=,u_2=,h_2=,x_2=$

For the process change, determine

$s=s_2-s_1=$

$u=u_2-u_1=$

$h=h_2-h_1=$