Question

what fraction of the total energy required to turn ice at -10 °c into steam at 100 °c is used for phase changes rather than for heating?
-~95%
-~50%
-~15%
-~85%

Explanation:

Step1: Identify energy - heating and phase - change components

The process of turning ice at - 10°C into steam at 100°C involves three heating steps and two phase - change steps.

1. Heating ice from - 10°C to 0°C: $Q_1 = mc_{ice}\Delta T_1$, where $c_{ice}=2.09\space J/g\cdot^{\circ}C$ and $\Delta T_1 = 10^{\circ}C$.
2. Melting ice at 0°C: $Q_2 = mL_f$, where $L_f = 334\space J/g$.
3. Heating water from 0°C to 100°C: $Q_3 = mc_{water}\Delta T_2$, where $c_{water}=4.18\space J/g\cdot^{\circ}C$ and $\Delta T_2 = 100^{\circ}C$.
4. Vaporizing water at 100°C: $Q_4 = mL_v$, where $L_v = 2260\space J/g$.

The total energy $Q_{total}=Q_1 + Q_2+Q_3 + Q_4$.
The energy for heating is $Q_{heating}=Q_1 + Q_3=m(2.09\times10 + 4.18\times100)=m(20.9 + 418)=m\times438.9$.
The energy for phase - changes is $Q_{phase}=Q_2 + Q_4=m(334 + 2260)=m\times2594$.

Step2: Calculate the fraction

The fraction $f=\frac{Q_{phase}}{Q_{total}}=\frac{Q_2 + Q_4}{Q_1 + Q_2+Q_3 + Q_4}=\frac{2594}{438.9 + 2594}\approx\frac{2594}{3032.9}\approx0.85 = 85\%$.

Answer:

~85%