Question

Because of its metabolic processes, your body continually emits thermal energy. Suppose that the air in your bedroom absorbs all of this thermal energy during the time you sleep at night (8.0 hours). Assume your metabolic rate to be P = 120 J/s. Estimate the temperature change you expect in this air. Let the volume of your room be 36 m2 and Heat capacity of air is 1000 J/kg C.

Answer 1

77.83783 °C

Step-by-step explanation:

V = Volume of room = 36 m²

c = Heat capacity = 1000 J/kg C

P = Power = 120 J/s = 120 W

t = Time = 8 hours

`\rho` = Density of air = 1.225 kg/m³

`\Delta T` = Change in temperature

Density is given by

`\rho=(m)/(V)\\\Rightarrow m=\rhoV\\\Rightarrow m=1.225* 36\\\Rightarrow m=44.1\ kg`

Heat is given by

`Q=mc\Delta T\\\Rightarrow Pt=mc\Delta T\\\Rightarrow \Delta T=(Pt)/(mc)\\\Rightarrow \Delta T=(120* 8* 3600)/(44.4* 1000)\\\Rightarrow \Delta T=77.83783^(\circ)C`

The temperature change you expected in this air 77.83783 °C