Question

We go out to sunbathe on a warm summer day. If we soak up 80 British thermal units per hour​ [BTU/h] of​ energy, how much will the temperature of 65 comma 000​-gram person increase in 2 hours ​[h] in units of degrees Celsius​ [°C]? We assume that since our bodies are mostly water they have the same specific heat as water ​(4.18 joules per gram degree Celsius​ [J/(g degrees Upper C​)]).

Answer 1

Answer:

0.62127°C

Explanation:

$1\ BTU=1055\ J$

$80\ BTU/h=80\times 1055=84400\ J/h$

Heat absorbed by body in 2 hours

$Q=84400\times 2\\\Rightarrow Q=168800\ J$

m = Mass of person = 65000 g

c = Specific heat of water = 4180 J/kg°C

$\Delta T$ = Change in temperature

Heat is given by

$Q=mc\Delta T\\\Rightarrow 168800=65\times 4180\times \Delta T\\\Rightarrow \Delta T=\dfrac{168800}{65\times 4180}\\\Rightarrow \Delta T=0.62127\ ^{\circ}C$

The increase in temperature will be 0.62127°C