Question

In situations in which the brain is deprived of oxygen, such as in a heart attack or traumatic brain injury, irreversible damage to the brain can happen very quickly. It's been proposed that cooling the body of a patient after cardiac arrest or traumatic brain injury may help protect the brain against long-term damage, perhaps by reducing the metabolic rate and thus the oxygen demand of the brain.

In order to achieve some protection for the brain without causing other undesired physiological effects such as disruptions to heart rhythms, the goal is to reduce the core body temperature from its normal value of 37 ∘C to between 30 ∘C and 35 ∘C. Animal experiments have shown some promising results, and human trials are being done. In one trial, 95% of patients had their core temperature reduced to 34 ∘C in 2.0 hours. To cool the body this quickly, each patient was placed between two cooled blankets, one above the patient and one below. Water and alcohol were sprayed on the patient, and any skin that wasn't covered by the top blanket was exposed to the environment.

For a patient in a typical hospital setting, the most important mechanism of heat loss is radiation. How does the power radiated by a patient change when the skin temperature drops from 34 ∘C to 33 ∘C, assuming no other changes?

A. It’s now 99% of what it originally was.

B. It’s now 89% of what it originally was.

C.It doesn’t change.

D.It’s now 97% of what it originally was

Answer 1

Using Stefan-Boltzmann law, power radiated is given as,
P = eAT⁴
Where is Stefan's constant, e is the emissivity of the human body, A is the area of the human body and T is the temperature in Kelvin.
P = KT⁴, where K = eA, which is a constant.
Initially, T = 34 ^oC = 307.15 K
Pi = K x (307.15)⁴
= 8900247394.56 K

Final power radiated, Pf = K x (306.15)⁴
= 8784904710.59 K

Pf/Pi = 8784904710.59 K / 8900247394.56 K
= 0.987
= 99 %
So Pf is 99% of initial power radiated