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**Problem**A person makes iced tea by mixing 500 g of hot tea (essentially water) with an equal mass of ice at its melting point. Assume the mixture has negligble energy exchanges with its environment. If the teas initial tempurature is T_i=90 deg celsius...when thermal equillibrium is reached what are (a) the mixtures final tempurature T_f and the remaining mass m_f of the ice?

**Relevant Eqs**Since

*the mixture has negligble energy exchanges with its environment*, [tex]\sum Q=0[/tex]

[tex]Q=mc\Delta T[/tex] and [tex]Q=mL_f[/tex]

**My crappy reasoning skills**

So I initially have: [tex] m_{w}=500g @ 90^{\circ}\stackrel{Q_1=(mc_w\Delta T)}{\rightarrow} T_f[/tex]

[tex]m_2= 500g@0^{\circ}\stackrel{Q_2=m_2L_f}{\rightarrow}T_f[/tex]

and I think I need a 3rd Q where :[tex]Q_3=(mc\Delta T)[/tex]

So I have 500g Water at 90 C--->T_f

500g Ice at 0 C----> some mass of water at 0 C

and then some mass of Water at 0 C--->T_f

Here is where I am getting all confused. Can anyone help point me in the right direction?

Casey