A person makes iced tea by adding ice to $1\mathrm{.}8$ kg of hot tea, initially at $80$C$.$ The initial temperature of ice is at $0$C$.$ The final mixture is $10$C$.$ The specific heat of water $($and tea$)$ is $4186$ J$/$kg $$ K$,$ and the latent heat of fusion of ice is $3\mathrm{.}34105$J$/$kg$.$

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Which of the following is correct?

Question $1$ options:

ice undergoes only temperature change but no phase transition

ice gain heat from the hot water

ice lose heat to the hot water

ice undergoes only phase transition and no temperature change