Question

According to kinetic-molecular theory, if the temperature of a gas is raised from 100 °c to 200 °c, the average kinetic energy of the gas will ________.

Answer 1

Actually the Kinetic Energy, which is also known as the energy of motion is directly proportional to temperature. So the higher the temperature is, the faster the gas particles move so they have possess more kinetic energy.

This temperature is in absolute units so we convert to Kelvin:

200 C = 473.15 K

100 C = 373.15 K

 

So the amount increase is:

473.15 / 373.15 = 1.268

 

It will increase by a factor of 1.268 or 126.8%

Answer 2

The average kinetic energy of the gas will increase by a factor of 1.27

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Further explanation

The Ideal Gas Law that needs to be recalled is:

$\large {\boxed {PV = nRT} }$

P = Pressure (Pa)

V = Volume (m³)

n = number of moles (moles)

R = Gas Constant (8.314 J/mol K)

T = Absolute Temperature (K)

Let us now tackle the problem !

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Given:

initial temperature of the gas = T₁ = 100°C = 373 K

final temperature of the gas = T₂ = 200°C = 473 K

Asked:

ratio of average kinetic energy of the gas = Ek₁ : Ek₂

Solution:

$Ek_1 : Ek_2 = \frac{3}{2}kT_1 : \frac{3}{2}kT_2$

$Ek_1 : Ek_2 = T_1 : T_2$

$Ek_1 : Ek_2 = 373 : 473$

$Ek_2 = \frac{473}{373} Ek_1$

$Ek_2 \approx 1.27 \times Ek_1$

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Conclusion:

The average kinetic energy of the gas will increase by a factor of 1.27 if the temperature of a gas is raised from 100°C to 200°C.

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Learn more

• Minimum Coefficient of Static Friction : https://brainly.com/question/5884009
• The Pressure In A Sealed Plastic Container : https://brainly.com/question/10209135
• Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454

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Answer details

Grade: High School

Subject: Physics

Chapter: Pressure