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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) at12.0{\rm ^{\circ} C}.

A.)What will be the person's body temperature T_final after equilibrium is attained? Ignore any heating by theperson's metabolism. The specific heat capacity of a human body is3480 {\rm J/kg \cdot K} .

B.)Is the change in the person's body temperature great enoughto be measured by a medical thermometer? (A high-quality medicalthermometer can measure temperature changes as small as0.1{\rm ^{\circ}C} or less.) yes or no

Respuesta :

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!!!

boffeemadrid

The equilibrium temperature is required and to find whether the temperature change can be measured by a thermometer is required.

The temperature is 310 K.

Yes, the thermometer can measure the temperature difference.

[tex]m_1[/tex] = Mass of person = 70 kg

[tex]c_1[/tex] = Specific heat of person = 3480 J/kg K

T = Equilibrium temperature

[tex]T_1[/tex] = Temperature of person = [tex]37\ ^{\circ}\text{C}+273.15 =310.15\ \text{K}[/tex]

[tex]1\ \text{L}=1\ \text{kg}[/tex] of water

[tex]m_2[/tex] = Mass of water = [tex]0.355\ \text{kg}[/tex]

[tex]c_2[/tex] = Specific heat of soft drink mostly water = [tex]4186\ \text{J/kg K}[/tex]

[tex]T_2[/tex] = Temperature of soft drink = [tex]12\ ^{\circ}\text{C}=285.15\ \text{K}[/tex]

The heat equation is

[tex]m_1c_1(T-T_1)=m_2c_2(T_2-T)\\\Rightarrow m_1c_1T-m_1c_1T_1=m_2c_2T_2-m_2c_2T\\\Rightarrow T=\dfrac{m_2c_2T_2+m_1c_1T_1}{m_1c_1+m_2c_2}\\\Rightarrow T=\dfrac{0.355\times 4186\times 285.15+70\times 3480\times 310.15}{70\times 3480+0.355\times 4186}\\\Rightarrow T=310\ \text{K}[/tex]

The temperature difference is [tex]T_1-T=310.15-310=0.15\ \text{K}=0.15\ ^{\circ}\text{C}[/tex]

Yes, the thermometer can measure the temperature difference.

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