Question

Show that the average kinetic energy of molecules of a gas is directly proportional
to the absolute temperature of the gas​

Answer 1

Answer:

According to kinetic theory of gases, the pressure .P. exerted by one mole of an ideal gas is

P=

1

3

ρC2 where ρ is density of the gas.

∴P=

1

3

M

V

C2⇒PV=

1

3

MC2

But PV=RT for one mole of ideal gas.

∴

1

3

MC2=RT⇒

1

3

M

NA

C2=

R

NA

T=KBT

(∴KB=

R

NA

)

(or)

1

2

mC2=

3

2

KBT⇒

1

2

mC2∝T

But, 1/2 mC^(2)` is average translational kinetic energy per molecule of a gas.

Therefore, average kinetic energy of molecule of an ideal gas is directly proportion to the absolute temperature of the gas.

Answer 2

Explanation:

According to kinetic theory of gases, the pressure .P. exerted by one mole of an ideal gas is <br>

where

is density of the gas. <br>

<br> But

for one mole of ideal gas. <br>

<br>

<br> (or)

<br> But, 1/2 mC^(2)