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A sports trainer applies an ice bag to the back of an injured athlete. Calculate the heat in kcal that is absorbed if 185 g of ice at 0.0 ∘C is placed in an ice bag, melts, and rises to body temperature of 37.0 ∘

c. (For water, 80. cal (334 J) is needed to melt 1 g of ice or must be removed to freeze 1 g of water.)

2 Answers

4 votes

Final answer:

To calculate the heat absorbed when 185 g of ice at 0.0 °C melts and warms to 37 °C, you must add the heat of fusion for melting the ice, which is 14.8 kcal, to the heat needed to raise the temperature of the water to 37 °C, which is 6.845 kcal, for a total of 21.645 kcal.

Step-by-step explanation:

The question is asking to calculate the amount of heat in kcal absorbed when 185 grams of ice at 0.0 °C melts and then is raised to the body temperature of 37.0 °C. To find this, we need to consider both the heat of fusion to melt the ice and the specific heat capacity of water to increase its temperature.

First, we use the heat of fusion for ice, which is 80 cal/g, to find how much heat is required to melt 185 g of ice:

(185 g) × (80 cal/g) = 14800 cal

Now, convert calories to kcal:

14800 cal ÷ 1000 cal/kcal = 14.8 kcal

This is the heat absorbed to just melt the ice. Next, we need to calculate the heat absorbed to raise the temperature from 0.0 °C to 37 °C:

The specific heat capacity of water is 1 cal/g°C, so the heat required is:

(185 g) × (1 cal/g°C) × (37 °C) = 6845 cal

Convert to kcal:

6845 cal ÷ 1000 cal/kcal = 6.845 kcal

Then add both parts:

14.8 kcal (melting) + 6.845 kcal (raising temperature) = 21.645 kcal

So the total heat absorbed by the ice and then water is 21.645 kcal.

User Zoheb
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2 votes

Amount of heat for melting the ice.

Q_1 = mL

Where m is mass

L is latent heat of ice

S is specific heat


= 185 (80) = 14800 cal

Amount of heat for rising the temperature of ice to 37 C^0.


For 0 C^0 to 37 C^0


Q_2  = m s dT


= 185 (540) (37) = 3696.3 * 10^3 cal

Q = Q1 + Q2


= 14800 + 3696.3 * 10^3 = 3711.11 * 10^3 cal

Thus, 3711.11 * 10^3 cal of energy is required for reaching the temperature of ice to 37 C^0

User Dansimau
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6.6k points