The Ideal Gas Law is expressed as \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the absolute temperature in Kelvin.
When you increase the temperature (\( T \)) of a gas while keeping the volume (\( V \)) constant, the pressure (\( P \)) will increase. This is because, according to the Ideal Gas Law, if \( n \) and \( V \) remain constant and \( T \) increases, \( P \) must also increase to maintain the equality of the equation.
Effects on Particle Speed:
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Particle Speed Increases: The average kinetic energy of gas particles is directly related to the temperature. As you increase the temperature, the average kinetic energy of the gas particles increases. The average speed of the gas particles, which can be expressed as \( \text{KE} = \frac{1}{2}mv^2 \) (where \( m \) is mass and \( v \) is speed), increases, resulting in particles moving faster.
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Heavy vs. Light Gas Particles: The relationship between temperature and speed doesn't depend on the mass of the individual gas particles. While lighter gas particles (like helium) will tend to move faster than heavier particles (like argon) at the same temperature, the overall increase in temperature will affect both particle types.
Summary:
- When you increase the temperature of a container with both heavy and light gas particles at constant volume, the pressure will increase.
- The average speed of all gas particles will increase due to the rise in temperature, but lighter gas particles will have a higher average speed compared to heavier gas particles at the same temperature.
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