*Notes to a video lecture on http://www.unizor.com*

__Problem 1__

How much kinetic energy have all the molecules in the room?

How fast should an average size car move to have this amount of kinetic energy?

Assume the following:

(a) the room dimensions are

*4*x

*4*x

*3 meters*(that is,

*);*

**V=48m³**(b) normal atmospheric pressure is

*100,000 Pascals*(that is,

*);*

**p=100,000N/m²**(c) a mass of an average size car is

*2,000 kg*(that is,

*).*

**M=2,000kg***Solution*

From the lecture on

*Kinetics of Ideal Gas*we know the relationship between the pressure on the walls of a reservoir, volume of a reservoir and total kinetic energy of gas inside this reservoir:

**p = (2/3)E**_{tot }**/V**From this we derive a formula for total kinetic energy:

**E**_{tot}**= (3/2)·p·V**Substituting the values for pressure and volume, we obtain

**E**_{tot}**= (3/2)·100,000·48 =**

= 7,200,000(joules)= 7,200,000

The kinetic energy of a car is

**E = M·v²/2**Therefore, given the kinetic energy and mass, we can determine the car's speed:

**v = √2·E/M**Substituting calculated above

*for*

**E**_{tot}**=7,200,000**(J)*and the value for mass*

**E***, we obtain*

**M=2,000**(kg)

**v = √2·7,200,000/2,000 ≅**

≅ 85(m/sec)≅ 85

**≅**

≅ 306(km/hour)≅ 306

**≅**

≅ 190(miles/hour)≅ 190

__Problem 2__

Given the temperature, pressure and volume of the air in a room, determine the number of gas molecules in it.

Assume the following:

(a) the room dimensions are

*4*x

*4*x

*3 meters*(that is,

*);*

**V=48m³**(b) normal atmospheric pressure is

*100,000 Pascals*(that is,

*);*

**p=100,000=10**^{5}N/m²(c) temperature is

*20°C*(that is,

*).*

**T=20+273=293°K***Solution*

Recall the combined law of ideal gas

**p·V/T = k**_{B}**·N = const**where

*is Boltzmann's constant and*

**k**_{B}**= 1.381·10**^{−23}(J/°K)*is the number of gas molecules in a reservoir.*

**N**From this we derive the number of molecules

**N = p·V/(k**_{B}**·T)**Substituting the values,

**N = 10**^{5}·48/(1.381·10^{−23}·293) = 0.12·10^{28}It's a lot!

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