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/kg⋅C∘, the latent heat of fusion is 333 kJ/kg, the specific heat of water is 4186 J/kg⋅C∘

Calculate the energy absorbed from a climber's body if he melts 0.70 kg of -15∘C snow using a stove and drink the resulting 0.70 kg of water at 2∘C, which his body has to warm to 37∘C.

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

Answer 1

Answer 2

To calculate the energy absorbed from a climber's body when melting snow and warming the resulting water, we need to consider the energy required for each step.

1. Melting the snow: The energy required to melt the snow is given by the latent heat of fusion. Energy = Mass * Latent heat of fusion

Mass of snow melted = 0.70 kg Latent heat of fusion = 333 kJ/kg = 333,000 J/kg

Energy absorbed from melting the snow = 0.70 kg * 333,000 J/kg = 233,100 J

2. Warming the water: The energy required to warm the water can be calculated using the specific heat of water. Energy = Mass * Specific heat * Change in temperature

Mass of water = 0.70 kg Specific heat of water = 4186 J/kg⋅C° Change in temperature = (37°C - 2°C) = 35°C

Energy absorbed from warming the water = 0.70 kg * 4186 J/kg⋅C° * 35°C = 105,350 J

Total energy absorbed from the climber's body = Energy from melting snow + Energy from warming water Total energy absorbed = 233,100 J + 105,350 J = 338,450 J

Therefore, the energy absorbed from the climber's body when melting 0.70 kg of -15°C snow and warming it to 37°C is approximately 338,450 J (to two significant figures).