Question

H
H
d
If
you
are trapped in a room of
dimension 10m x 10m x 10m, how
long can you survive? Assume
room is completely
sealed and nothing (not even air) can come
inside.
​

Answer 1

Answer:

The volume of air present in the room is 5×10×3=150 m

3

=150×10

3

litre (∵ 1 m

3

=1000 L)

The number of moles of air is calculated using the ideal gas equation.

n=

RT

PV

=

0.0821×293

1×150×10

3

=6.236×10

3

For 1 mole of air, (

∂T

∂H

)

P

=C

p

=

ΔT

ΔH

For n moles of air, ∴ΔH=n×C

p

×ΔT

Substitute values in the above expression,

ΔH=6.236×10

3

×

2

7

×8.314×(310−293)=3.085×10

6

J

Thus, the heat need to increase the temperature of the room to 37

∘

C is =3.085×10

6

J

The heat released by 50 people is =150×50 J/sec=7500 J/sec. This is the heat provided in 1 second.

∴ The time required to provide 3.085×10

6

J heat is

7500

1×3.085×10

6

=411.3 sec.

Hence, the correct option is B