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

Question #305380

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.


1
Expert's answer
2022-03-03T13:23:00-0500

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=12×10×3m350×0.2m3=350m3V = 12\times 10\times 3 m^3 - 50\times 0.2m^3 = 350m^3


Assuming the density of air to be ρ=1.225kg/m3\rho = 1.225kg/m^3, the mass of the air is m=ρVm = \rho V.

The amount of heat given in 10 minutes is:


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

The temperature difference is then:


ΔT=QCVm=QcvρV\Delta T = \dfrac{Q}{C_Vm} = \dfrac{Q}{c_v\rho V}

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


ΔT=1250kcal0.171kcal/kg/K1.225kg/m3350m317°C\Delta T = \dfrac{1250kcal}{0.171kcal/kg/K\cdot 1.225kg/m^3\cdot 350m^3} \approx 17\degree C

Thus, the final temperature:


T2=17°C+16°C=33°CT_2 = 17\degree C + 16\degree C = 33\degree C

Answer. 33°C33\degree C.


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