Question

Approximately 80% of the energy used by the body must be dissipated thermally. The mechanisms available to eliminate this energy are radiation, evaporation of sweat, evaporation from the lungs, conduction, and convection. In this question, we will focus on the evaporation of sweat alone, although all of these mechanisms are needed to survive. The latent heat of vaporization of sweat at body temperature (37∘C) is 2.42 × 106 J/kg and the specific heat of a body is approximately 3500 J/(kg⋅∘C)

A) To cool the body of a jogger of mass 100 kg by 2.3 ∘C , how much sweat has to evaporate?

Answer 1

To cool a jogger weighing 100 kg by 2.3°C, approximately 0.333 kg of sweat needs to evaporate. This is calculated by using the specific heat of the body and the latent heat of vaporization of sweat.

Step-by-step explanation:

To calculate the amount of sweat that needs to evaporate to cool the body of a jogger by 2.3°C, we need to know two things: the specific heat of the body and the amount of heat that needs to be removed (which is the product of the jogger's mass, the specific heat, and the temperature change). The specific heat is given as approximately 3500 J/(kg°C), and the latent heat of vaporization of sweat at body temperature is 2.42 × 106 J/kg.

The total amount of heat that needs to be removed can be calculated by:

Heat removed (Q) = mass of jogger (m) × specific heat (c) × temperature change (ΔT)

Substituting the given values we get:

Q = 100 kg × 3500 J/(kg°C) × 2.3°C = 805,000 J

To find out how much sweat must evaporate:

Mass of sweat (m_sweat) = Heat removed (Q) / latent heat of vaporization (Λ_v)

Hence:

m_sweat = 805,000 J / 2.42 × 106J/kg = 0.333 kg

So, to cool down by 2.3°C, the jogger would need to evaporate approximately 0.333 kg of sweat.