In an emergency, it is sometimes the practice of medical professionals to immers

Question

In an emergency, it is sometimes the practice of medical professionals to immerse a patient who suffers from heat stroke in an ice bath, a mixture of ic and water in equilibrium at 0C, in order to reduce her body temperature.

a) if a 72 kg patient whose body temperature is 41.6C must have her temperature reduced to the normal range, how much heat must be removed? (assume her normal temperature is 37C)

b) if she is placed in a bath containing 8.1 kg of ice, will ther be ice remaining in the bath when her body temperature is 37.0C? yes or no

if so, how much of the ice is remaining?

if not, what will be the final temperature?

Explanation / Answer

a) Heat removed = m*S*(Ti - Tf))

S = 3470 J/Kg C

Heat = 72 * 3470*(41.6 - 37) = 1.15 MJ

b) ice = 8.1 kg

Latent heat of ice L = 334*10^3 J/Kg

Heat absorbed for melting = mL = 8.1*334*10^3 = 2.7MJ

This much heat is required to melt 8.1 Kg of ice while the body rest at 37.0 C

Since the required heat is less than heat removed hence the body temperature will reduce more

If body temperature reduces to 0

Heat removed = 10.39 MJ

this is more than sufficient to melt ice

So ice will melt and body temperature will be greater than 0 but less than 37

Let it be T

mL + m*S(ice)*T = 72*S*(41.6 - T)

S(ice) = 2.09*10^3 J/KgC

=> 8.1*334*10^3 + 8.1*2.09*10^3 *T = 72*3470*(41.6 - T)

=>0.267*10^6 T = 7.69*10^6

=> T = 28.82 degree C

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