Question

Calculate how many grams of ice at 0°C would be melted by 100 g of 100°C steam. Hint: heat will be transferred from the steam to the ice in two processes: (a) the steam will condense into liquid, and (b) that liquid will transfer heat until it is at the freezing point of water. Note that for water: Lf = 80 cal/g, and Lv = 540 cal/g

Answer 1

Answer on Question #64873-Physics-Other

Calculate how many grams of ice at $0{}^{\circ}\mathrm{C}$ would be melted by $100\mathrm{g}$ of $100{}^{\circ}\mathrm{C}$ steam. Hint: heat will be transferred from the steam to the ice in two processes: (a) the steam will condense into liquid, and (b) that liquid will transfer heat until it is at the freezing point of water. Note that for water: $\mathrm{Lf} = 80\mathrm{cal / g}$, and $\mathrm{Lv} = 540\mathrm{cal / g}$

Solution

Heat will be transferred from the steam to the ice in two processes: (a) the steam will condense into liquid, and (b) that liquid will transfer heat until it is at the freezing point of water.

$$Q _ {i c e} = Q _ {a} + Q _ {b}$$ $$m _ {i c e} L _ {f} = m _ {w a t e r} L _ {v} + m _ {w a t e r} c _ {w a t e r} \Delta T$$ $$m _ {i c e} = \frac {m _ {w a t e r}}{L _ {f}} (c _ {w a t e r} \Delta T + L _ {v}) = \frac {1 0 0 g}{8 0 \frac {\mathrm {c a l}}{\mathrm {g}}} \Big (5 4 0 \frac {c a l}{g} + 1 \frac {\mathrm {c a l}}{\mathrm {g} {}^ {\circ} \mathrm {C}} (1 0 0 - 0) {}^ {\circ} \mathrm {C} \Big) = 8 0 0 g.$$

Answer: $800g$

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