How to set up the balance equation

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Text page showing Problem 7-3, containment pressure increase due to residual core heat, with conditions after 1 hour: water mixture mass 1.56(10^6) kg, quality 0.0249, air mass 5.9(10^5) kg, nitrogen mass 1.0(10^3) kg, initial temperature 381.6 K, and gas properties.


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Three equations: m_w(u_w2 - u_w1) + m_a c_va(T_2 - T_a1) = Q_n-wsysr - Q_c-st; then m_w u_w1 = m_wa u_wa1 + m_wsys u_wsys1; and m_w u_w2 = (m_wa + m_wsys) u_w2.
I have problem with these two questions, can you give me a hint and help to understand it, I do understand problem 7-3 but i have problem with applying the equastion, I don't understand to 7-2 but i knw we have to have an addition term for the ice in the given balance equastion, can anyone help me with it


here its sorry
 
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  • Textbook problem 7-2, Ice condenser containment analysis: calculate minimum mass of ice to keep final containment pressure below 0.4 MPa, with given initial conditions and properties for air, ice and water fusion; answer 1.77(10^5) kg of ice.
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matt222 said:
I have problem with these two questions, can you give me a hint and help to understand it, I do understand problem 7-3 but i have problem with applying the equastion, I don't understand to 7-2 but i knw we have to have an addition term for the ice in the given balance equastion, can anyone help me with it
I don't see problem 7-2.
 


In 7-2, there is containment at a given volume and pressure (1 atm). If there is a rupture of the primary system (initially at saturated liquid conditions at 15.5 MPa), it will pressurize the containment. There has to be enough ice available to cool the liquid water from the primary system, such that the vapor and air in the containment do not exceed the pressure limit of 0.4 MPa.

The ice is at -10°C, so it must heat up to melting temp, then change phase from liquid to solid, and then heat up to some equilibrium with the primary water.

One can neglect the volume of ice by assuming that it's volume doesn't change much going from ice to liquid in containment.
 


But the problem now how to set up the balance equation! How to include the ice in the equation and we have fusion heat mixed me up!