Calculating Final Body Temperature After Soda Consumption

[doggieslover]

Before going in for an annual physical, a 70.0-{\rm kg} person whose body temperature is 37.0{\rm ^{\circ} C} consumes an entire 0.355-{\rm liter} can of a soft drink (which is mostly water) at 12.0{\rm ^{\circ} C}.

Part A
What will be the person's body temperature T_final after equilibrium is attained? Ignore any heating by the person's metabolism. The specific heat capacity of a human body is 3480 {\rm J/kg \cdot K}.

I tried m_1c_1deltaT_1+m_2c_2deltaT_2=0
I got stuck here:
(70kg)(3480J/kgK)(T_f-37) + (70kg)(what is the specific heat for soda?)(Is this just 12C?)

Part B
Is the change in the person's body temperature great enough to be measured by a medical thermometer? (A high-quality medical thermometer can measure temperature changes as small as 0.1{\rm ^{\circ}C} or less.)

yes or no?

I don't really get what they are asking here, I want to say NO, because logically speaking, drinking soda wouldn't lower your body temperature drastically. . . ?

 

[Redbelly98]

Part A.

I have 2 observations:

1. The problem statement says what material the soda is (mostly) made of, so use the specific heat for that material.

2. The soda is not 70 kg. You'll have to figure out its mass from the information given in the problem statement.

 

[thomate1]

Part A:

To calculate the final body temperature, we can use the principle of conservation of energy. The total energy of the system before and after the soda consumption must be equal.

We can set up the equation as follows:

m1c1(T1 - T_final) + m2c2(T2 - T_final) = 0

Where:
m1 = mass of the person (70.0 kg)
c1 = specific heat capacity of human body (3480 J/kg*K)
T1 = initial body temperature (37.0°C)
T_final = final body temperature (unknown)
m2 = mass of the soda (0.355 kg)
c2 = specific heat capacity of soda (unknown)
T2 = initial temperature of soda (12.0°C)

Solving for T_final, we get:

T_final = (m1c1T1 + m2c2T2) / (m1c1 + m2c2)

Substituting the given values, we get:

T_final = (70.0 kg * 3480 J/kg*K * 37.0°C + 0.355 kg * c2 * 12.0°C) / (70.0 kg * 3480 J/kg*K + 0.355 kg * c2)

We are given that the soda is mostly water, so we can assume that the specific heat capacity of the soda is similar to that of water, which is 4186 J/kg*K. Substituting this value, we get:

T_final = (70.0 kg * 3480 J/kg*K * 37.0°C + 0.355 kg * 4186 J/kg*K * 12.0°C) / (70.0 kg * 3480 J/kg*K + 0.355 kg * 4186 J/kg*K)

Simplifying, we get:

T_final = 37.08°C

Therefore, the person's final body temperature after drinking the soda will be 37.08°C.

Part B:

No, the change in the person's body temperature is not great enough to be measured by a medical thermometer. The change in temperature is only 0.08°C, which is much smaller than the precision of a high-quality medical thermometer (0.1°C or less). Therefore, the change in temperature would not be detected by the thermometer.