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 is 2100 J/kgC , the latent heat of fusion is 333 kJ/kg , the specific heat of water is 4186 J/kgC .

Part A

Calculate the energy absorbed from a climber's body if he eats 0.90 kg of -15C snow which his body warms to body temperature of 37C .

Part B

Calculate the energy absorbed from a climber's body if he melts 0.90 kg of -15C snow using a stove and drink the resulting 0.90 kg of water at 2C , which his body has to warm to 37C .

Explanation / Answer

Specific heat capacity of snow (ice) { 2.1 kJ/kg.°C }
Specific heat capacity of water { 4.2 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 0.9kg of ice from -15°C to ice at 0°C
+
Energy to change 0.9 kg of ice at 0°C to 1 kg at water at 0°C
+
Energy to raise temperature of 0.9kg of water from 0°C to 37°C

= 0.9 kg * (2.1 kJ/kg.°C * 15°C + 333 kJ/kg+ 4.2 kJ/kg.°C * 37°C)
= 467.91 kJ


(b)
Energy required to change 0.9 kg of water at 2°C to water at 35°C
= 0.9 kg * 4.2 kJ/kg.°C * (37 - 2)°C
= 132.3 KJ

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