Kinetic Theory of Gases homework

Summary: In summary, the conversation is about finding the value of the specific heat ratio (r) for a mixture of one mole of a monoatomic gas with a specific heat ratio of 5/3 and one mole of a diatomic gas with a specific heat ratio of 7/3. This value can be found by calculating the ratio of specific heats (C(p)/C(v)), which is the amount of heat energy needed to increase the temperature of one mole of the combined gas by one degree. This can also be thought of as the sum of the specific heats needed for 1/2 a mole of each gas separately.
  • #1
Amith2006
427
2
3)Sir,
Please help me with this problem.
# If one mole of a mono atomic gas(r = 5/3) is mixed with one mole of a
diatomic gas(r = 7/3),then what is the value of the r for the mixture?
In the above problem r = C(p)/C(v) = ratio of specific heats.
 
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  • #2
Amith2006 said:
3)Sir,
Please help me with this problem.
# If one mole of a mono atomic gas(r = 5/3) is mixed with one mole of a
diatomic gas(r = 7/3),then what is the value of the r for the mixture?
In the above problem r = C(p)/C(v) = ratio of specific heats.
Think of it this way: the specific heat(s) of the combined gas is the amount of heat energy needed to increase one mole of the combined gas' temperature by one degree. But that same amount of heat is simply the sum of the heats needed to increase the temperature of 1/2 a mole of each gas separately (by one degree).

AM
 
Last edited:

1. What is the Kinetic Theory of Gases?

The Kinetic Theory of Gases is a scientific theory that explains the behavior of gases at a microscopic level. It states that gases are composed of particles (atoms or molecules) that are in constant random motion and that the pressure of a gas is a result of the collisions between these particles and the walls of the container.

2. What are the assumptions of the Kinetic Theory of Gases?

The assumptions of the Kinetic Theory of Gases include:

  • Gases are composed of particles that are in constant, random motion.
  • The size of the particles is negligible compared to the size of the container.
  • The particles do not interact with each other, except during collisions.
  • The collisions between particles and the walls of the container are perfectly elastic.
  • The average kinetic energy of the particles is directly proportional to the temperature of the gas.

3. How does the Kinetic Theory of Gases explain the relationship between pressure, volume, and temperature?

The Kinetic Theory of Gases states that the pressure of a gas is directly proportional to the average kinetic energy of its particles. When the temperature of a gas increases, the average kinetic energy of its particles also increases, leading to an increase in pressure. Similarly, when the volume of a gas is decreased, the particles have less space to move around, resulting in an increase in collisions and therefore an increase in pressure.

4. What is the equation for the Kinetic Theory of Gases?

The Kinetic Theory of Gases can be mathematically represented by the equation:

PV = 1/3 * N * m * v^2, where:

  • P is the pressure of the gas
  • V is the volume of the gas
  • N is the number of particles
  • m is the mass of each particle
  • v is the root mean square speed of the particles

5. What are some real-life applications of the Kinetic Theory of Gases?

The Kinetic Theory of Gases has many practical applications, including:

  • Understanding the behavior of gases in chemical reactions and industrial processes
  • Designing and improving gas-powered engines and turbines
  • Explaining the ideal gas law and its use in various fields such as meteorology and gas laws
  • Developing gas laws and equations for predicting the behavior of gases under different conditions

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