Answer:
A) The person's body temperature T_final after equilibrium is attained = 36.85°C
B) The change in the person's temperature after equilibrium is attained = 0.15°C
A high-quality medical thermometer can measure temperature changes as small as 0.1°C, hence, YES, it would detect the minute drop by 0.15°C too.
Explanation:
If we assume that the soft drink has the same density as water (since it is stated in the question that it is mostly water).
Density of water = 1 g/mL = 1 kg/L
Ignoring any heating by the person's metabolism,
A) So, heat lost by the human body = heat gained by the soft drink as it attains thermal equilibrium with the human body
Let the final temperature of the human body + soft drink set up be T
Heat lost by the human body = mCΔT
m = mass of the human body = 70.0 kg
C = Specific heat capacity of the human body = 3480 J/kg.K
ΔT = Temperature change of the human body = 37 - (Final temperature) = 37 - T
Heat lost by the body = 70 × 3480 × (37 - T)
= (9,013,200 - 243,600T) J
Heat gained by soft drink = mCΔT
m = mass of the soft drink = density × volume = 1 × 0.355 = 0.355 kg
C = specific heat capacity of the soft drink = specific heat capacity of the soft drink = 4182 J/kg.K
ΔT = (final temperature) - 12 = (T - 12)
Heat gained by the soft drink = 0.355 × 4182 × (T - 12) = (1,484.61T - 17,815.32) J
heat lost by the human body = heat gained by the soft drink as it attains thermal equilibrium with the human body
(9,013,200 - 243,600T) = (1,484.61T - 17,815.32)
9,013,200 + 17,815.32 = 1,484.61T + 243,600T
9,031,015.32 = 245,084.61T
T = (9,031,015.32/245,084.61)
= 36.8485614825 = 36.85°C
B) The change in the person's temperature = 37 - 36.85 = 0.15°C
A high-quality medical thermometer can measure temperature changes as small as 0.1°C, hence it would detect the minute drop by 0.15°C too.
Hope this Helps!!!
