Answer to Question #213402 in Molecular Physics | Thermodynamics for Yomna

Question

A rigid tank of volume 24 liters contains 0.2 kg of H2O originally at 2 bar. Find 

specific volume and initial temperature. What are the phases present (solid, 

liquid, vapor?). The tank was heated until its pressure reached 20 bar. Find work 

and heat exchanged during this process as well as final temperature

Answer 1

Solution.

$V=24\sdot10^{-3}m^3;$

$m=0.2kg;$

$P_1=2\sdot10^5Pa;$

$P_2=20\sdot10^5Pa;$

$\dfrac{V}{m}=\dfrac{24\sdot10^{-3}}{0.2}=0.12m^3/kg;$

$M=18\sdot10^{-3}kg/mol;$

$PV=\dfrac{m}{M}RT\implies T_1=\dfrac{PVM}{mR};$

$T_1=\dfrac{2\sdot10^{5}\sdot24\sdot10^{-3}\sdot18\sdot10^{-3}}{0.2\sdot8.31}=52K;$

$\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2};$

$T_2=\dfrac{T_1P_2}{P_1}=\dfrac{520\sdot20\sdot10^5}{2\sdot10^5}=520K;$

$W=0;$

$Q=c_Vm(T_2-T_1);$

$c_V=\dfrac{i}{2} R$

$Q=20.8\sdot0.2\sdot468=1947J;$

Answer: $\dfrac{V}{m}=0.12m^3/kg;$

$T_1=52K;$

$W=0;$

$Q=1947J.$