Charles has increased his activity by doing more exercise. After a session of using weights, he has a sore arm. An ice bag is filled with 125 g of ice at 0 °C. How much heat, in kilojoules, is absorbed to melt the ice and raise the temperature of the water to body temperature, 37.0 °C?

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**STEP 1 State the given and needed quantities.**

**STEP 2 Write a plan to convert the given quantity to the needed quantity.**

Total heat = kilojoules needed to melt the ice at 0 °C and heat the water from 0 °C (freezing point) to 37.0 °C

**STEP 3 Write the heat conversion factors and any metric factor.**

1 \space g \space of \space H_{2}O \space (s \longrightarrow l) = 334 \space J SH_{water}= \frac{4.184 \space J}{g \space °C} 1 \space kJ = 1000 \space J

\frac{334 \space J}{1 \space g \space H_{2}O} and \frac{1 \space g \space H_{2}O}{334 \space J} \frac{4.184 \space J}{g\space °C} and \frac{g\space °C}{4.184 \space J} \frac{1000 \space J}{1 \space kJ} and \frac{1 \space kJ}{1000 \space J}

**STEP 4 Set up the problem and calculate the needed quantity.**

∆*T* = 37.0 °C – 0 °C = 37.0 °C

Heat needed to change ice (solid) to water (liquid) at 0 °C:

Heat needed to warm water (liquid) from 0 °C to water (liquid) at 37.0 °C:

Heat = \underset{Three \space SFs}{125 \space \cancel {g}} \space \space\times \space \space \underset{Three \space SFs}{37.0 \space °\cancel {C}} \space \space\times \space \space\frac{\overset{Exact}{4.184 \space \cancel J} }{\underset{Exact}{\cancel g \space° \cancel {C }} } \space \space \times \space \space \frac{\overset{Exact}{1 \space kJ} }{\underset{Exact}{1000 \space \cancel J} }\space \space =\space \space \underset{Three \space SFs}{19.4 \space kJ}Calculate the total heat:

Melting ice at 0 °C 41.8 kJ

Heating water (0 °C to 37.0 °C) \frac{19.4 \space kJ}{}

Total heat needed 61.2 kJ

ANALYZE THE PROBLEM |
Given |
Need |
Connect |

125 g of ice at 0 °C |
total kilojoules to melt ice at 0 °C and to raise temperature of water to 37.0 °C |
combine heat from change of state (heat of fusion) and temperature change (specific heat of water) |

Question: 3.CC.4

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