A person's body temperature is controlled by the following.convective and radiative heat transfer to the surroundingssweatingrespiration by breathing surrounding air and exhaling it at approximately body temperatureblood circulation near the surface of the skinmetabolic rateMetabolic rate determines the rate of conversion of chemical to thermal energy within a person's body. The metabolic rate depends on the person's activity level. A unit commonly used to express the metabolic rate for an average person under sedentary conditions (per unit surface area) is called met; 1 met is equal to 58.2 W/m2. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)(a)How many square feet are equal to 1 square meter? ft2How many Btu/h are equal to 1 watt? Btu/hConvert 1 met (58.2 W/m2) to Btu/(h · ft2). Btu/(h · ft2)(b)Calculate the amount of energy dissipated by an average adult person sleeping for 7 hours if he or she generates 0.8 mets and has a body surface area of 18.8 ft2. Express your results in Btu and joules (1 Btu = 1,055 joules).Express the amount of energy in Btu. Show all conversion steps. = (0.8 mets) Btuh · ft21 met( ft2)( h) = BtuExpress the amount of energy in joules. Show all conversion steps.= (the energy in Btu) joules1 Btu = J
Question
A person's body temperature is controlled by the following.convective and radiative heat transfer to the surroundingssweatingrespiration by breathing surrounding air and exhaling it at approximately body temperatureblood circulation near the surface of the skinmetabolic rateMetabolic rate determines the rate of conversion of chemical to thermal energy within a person's body. The metabolic rate depends on the person's activity level. A unit commonly used to express the metabolic rate for an average person under sedentary conditions (per unit surface area) is called met; 1 met is equal to 58.2 W/m2. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)(a)How many square feet are equal to 1 square meter? ft2How many Btu/h are equal to 1 watt? Btu/hConvert 1 met (58.2 W/m2) to Btu/(h · ft2). Btu/(h · ft2)(b)Calculate the amount of energy dissipated by an average adult person sleeping for 7 hours if he or she generates 0.8 mets and has a body surface area of 18.8 ft2. Express your results in Btu and joules (1 Btu = 1,055 joules).Express the amount of energy in Btu. Show all conversion steps. = (0.8 mets) Btuh · ft21 met( ft2)( h) = BtuExpress the amount of energy in joules. Show all conversion steps.= (the energy in Btu) joules1 Btu = J
Solution
(a)
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To convert square meters to square feet, we use the conversion factor 1 square meter = 10.764 square feet.
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To convert watts to Btu/h, we use the conversion factor 1 watt = 3.412142 Btu/h.
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To convert 1 met (58.2 W/m2) to Btu/(h · ft2), we first convert watts to Btu/h, then square meters to square feet. So, 58.2 W/m2 = 198.65 Btu/(h · m2) = 18.45 Btu/(h · ft2).
(b)
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To calculate the amount of energy dissipated by an average adult person sleeping for 7 hours, we first need to convert mets to Btu/(h · ft2). So, 0.8 mets = 14.76 Btu/(h · ft2).
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Then, we multiply this by the person's body surface area and the number of hours slept to get the total energy dissipated. So, (14.76 Btu/(h · ft2)) * (18.8 ft2) * (7 h) = 1946.656 Btu.
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To convert this to joules, we use the conversion factor 1 Btu = 1,055 joules. So, 1946.656 Btu = 2,053,621.68 joules.
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