High-altitude mountain climbers do not eat snow, but always melt it first with a

Question

High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from a climber's body under the following conditions. The specific heat of ice is2100 J/kgC, the latent heat of fusion is 333 kJ/kg,the specific heat of water is 4186 J/kgC.

A) Calculate the energy absorbed from a climber's body if he eats 0.50 kg of -15C snow which his body warms to body temperature of 37C.

Express your answer to two significant figures and include the appropriate units.

B) Calculate the energy absorbed from a climber's body if he melts 0.50 kg of -15C snow using a stove and drink the resulting 0.50 kg of water at 2C, which his body has to warm to 37C.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Specific heat capacity of snow (ice) { 2.1 kJ/kg.°C }
Specific heat capacity of water { 4.186 kJ/kg.°C }
Latent heat of fusion of ice { 333 kJ/kg }

Solve using:
Heat energy = mass * specific heat * change in temperature
Heat energy = mass * Latent heat of fusion

(a)
Total heat energy required =

Energy to raise temperature of 0.5 kg of ice from -15°C to ice at 0°C
+
Energy to change 0.5 kg of ice at 0°C to 0.5 kg at water at 0°C
+
Energy to raise temperature of 0.5 kg of water from 0°C to 37°C

= (0.5 kg * 2.1 kJ/kg.°C * 15°C) + (0.5 kg * 333 kJ/kg) + (0.5 kg * 4.186 kJ/kg.°C * 37°C)
= 15.75 kJ + 166.5 kJ + 77.7 kJ
= 260 kJ
= 2.6 * 10^5 J

(b)
Energy required to change 0.5 kg of water at 2°C to water at 35°C
= 0.5 kg * 4.186 kJ/kg.°C * (37 - 2)°C
= 72.255 kJ
= 0.72255 * 10^5 J

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