One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0°C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached 32.0°C. To treat a 70.0 kg patient, what is the minimum amount of ice (at 0°C) you need in the bath so that its temperature remains at 0°C? The specific heat of the human body is 3480 J/kg C°, and recall that normal body temperature is 37.0°C.

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Determine the amount of heat that needs to be removed from the patient's body to lower the temperature from 37.0°C to 32.0°C. Use the formula for heat transfer: \( Q = mc\Delta T \), where \( m \) is the mass of the patient, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Calculate the change in temperature \( \Delta T \) as \( 37.0°C - 32.0°C = 5.0°C \).

Substitute the known values into the heat transfer formula: \( Q = (70.0 \text{ kg})(3480 \text{ J/kg°C})(5.0°C) \). This will give you the total heat \( Q \) that needs to be removed from the patient's body.

To find the minimum amount of ice required, use the formula for the heat absorbed by the ice: \( Q = mL_f \), where \( m \) is the mass of the ice and \( L_f \) is the latent heat of fusion for ice, which is 334,000 J/kg.

Set the heat removed from the body equal to the heat absorbed by the ice: \( (70.0 \text{ kg})(3480 \text{ J/kg°C})(5.0°C) = m(334,000 \text{ J/kg}) \). Solve for \( m \) to find the minimum mass of ice needed.

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주요 개념

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Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. It is crucial in this problem to calculate the heat loss needed to lower the patient's body temperature from 37.0°C to 32.0°C. The specific heat capacity of the human body is given as 3480 J/kg°C, which will be used to determine the total heat energy that must be removed.

Heat Transfer

Heat transfer is the process of thermal energy moving from a hotter object to a cooler one. In this scenario, heat will transfer from the patient's body to the ice-water bath. Understanding this concept is essential to calculate how much ice is needed to absorb the heat lost by the patient, ensuring the bath remains at 0°C.

Latent Heat of Fusion

The latent heat of fusion is the amount of heat required to change a unit mass of a solid into a liquid without a temperature change. For ice, this is the energy needed to melt it at 0°C. This concept is vital to determine how much ice must melt to absorb the heat from the patient, ensuring the bath's temperature remains constant at 0°C.