Question

Physics Help? We all have had the experience that a room full of people always feels warmer than when the room is empty...

2.) We all have had the experience that a room full of people always feels warmer than when the room is empty. Ten people are in a 4.0 m x 6.0 m x 3.0 m room at 20° C. If each person gives off heat at a rate of about 100 W and there is no heat loss to the outside of the room, what is the temperature of the room after 10 min? At 20° C, the density of air is 1.2 kg m and its specific heat at constant pressure is 1005 J/kg/OC.

Answer 1

Rate of Heat given off by each person is, R= 100W

Then Heat given by each person in 10 min or (10 * 60) seconds is

   $Q= R \times t(seconds)= 100 \times 10 \times 60= 60000J$

And Total Heat given off by 10 people in the room is

   $Q_t= Q \times 10 = 60000 \times 10= 6 \times 10^5J$

Now Volume of the room is $V= (4.0 \times 6.0 \times 3.0)m^3= 72m^3$

Density of the air, $\rho= 1.2 kg/m^3$

Then Mass of air is $M= Volume \times \rho= 72 \times 1.2= 86.4 kg$

Given Specific Heat at constant pressure is $c_p= 1005 J/kg. ^{\circ} C$

Then Using the fornula,

Heat Gain,

Using given initial value of temperature and all other calculated values in above, we get

   $6 \times 10^6= (86.4)(1005)(T_{final}- 20)$

or    $T_{final}= 26.91 ^{\circ} C$ (ANS)