Answer to Question #305380 in Molecular Physics | Thermodynamics for Tobias Felix

Question

A group of 50 persons attended a secret meeting in a room 12m x 10m x 3m high. The

room is completely sealed off and insulated. Each person gives off 150 kcal/hr of heat

and occupies a volume of 0.2 cubic meters. The room has an initial pressure of 101.3

kpa and 16C. calculate the room temp after 10minutes.

Answer 1

The volume of the air in the room is the difference between the volume of the room and the total volume occupied by people:

$$V = 12\times 10\times 3 m^3 - 50\times 0.2m^3 = 350m^3$$

Assuming the density of air to be $\rho = 1.225kg/m^3$, the mass of the air is $m = \rho V$.

The amount of heat given in 10 minutes is:

$$Q = 150kcal/hr\times 1/6hrs\times 50 = 1250kcal$$

The temperature difference is then:

$$\Delta T = \dfrac{Q}{C_Vm} = \dfrac{Q}{c_v\rho V}$$

where $c_V = 0.171 kcal/kg/K$ is the specific heat capacity. Thus, obtain:

$$\Delta T = \dfrac{1250kcal}{0.171kcal/kg/K\cdot 1.225kg/m^3\cdot 350m^3} \approx 17\degree C$$

Thus, the final temperature:

$$T_2 = 17\degree C + 16\degree C = 33\degree C$$

Answer. $33\degree C$.