The equilibrium temperature of the system is required.
The equilibrium temperature of the mixture is [tex]18.48^{\circ}\text{C}[/tex].
[tex]m_i[/tex] = Mass of ice = 25 kg
[tex]m_s[/tex] = Mass of steam = 4 kg
[tex]T_i[/tex] = Temperature of ice = [tex]0^{\circ}\text{C}[/tex]
[tex]T_s[/tex] = Temperature of steam = [tex]100^{\circ}\text{C}[/tex]
[tex]L_f[/tex] = Latent heat of fusion = [tex]3.34\times 10^5\ \text{J/kg}[/tex]
[tex]L_v[/tex] = Latent heat of vaporization = [tex]2.23\times 10^6\ \text{J/kg}[/tex]
[tex]c_w[/tex] = Specific heat of water = [tex]4180\ \text{J/kg}^{\circ}\text{C}[/tex]
The heat balance of the system will be
[tex]m_iL_f+m_ic_w(T-T_i)=m_sL_v+m_sc_w(T_s-T)\\\Rightarrow m_iL_f+m_ic_wT-m_ic_wT_i=m_sL_v+m_sc_wT_s-m_sc_wT\\\Rightarrow T=\dfrac{m_ic_wT_i+m_sL_v+m_sc_wT_s-m_iL_f}{m_ic_w+m_sc_w}\\\Rightarrow T=\dfrac{25\times 4180\times 0+4\times 2.23\times 10^6+4\times 4180\times 100-25\times 3.34\times 10^5}{25\times 4180+4\times 4180}\\\Rightarrow T=18.49^{\circ}\text{C}[/tex]
The equilibrium temperature of the mixture is [tex]18.49^{\circ}\text{C}[/tex].
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