0.2.1 State what is meant by the internal energy of a gas. 0.2.2 Absolute zero of temperature can be interpreted in terms of the ideal gas laws or the kinetic energy of particles in an ideal gas. Describe these two interpretations of absolute zero of temperature. 0.2.3 A mixture of argon atoms and helium atoms is in a cylinder enclosed with a piston. The mixture is at a temperature of 310 K. Calculate the root mean square speed ( $c_{rms}$ ) of the argon atoms in the mixture. molar mass of argon = $4.0 imes 10^{-2} ext{ kg mol}^{-1}$ $c_{rms} = ext{________} ext{ m s}^{-1}$ 0.2.4 Compare the mean kinetic energy of the argon atoms and the helium atoms in the mixture. 0.2.5 Explain, in terms of the kinetic theory model, why a pressure is exerted by the gas on the piston. 0.2.6 The mixture of gases in the cylinder stays the same. Explain, using the kinetic theory model, two changes that can be made independently to reduce the pressure exerted by the gas.

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0.2.1 State what is meant by the internal energy of a gas - AQA - A-Level Physics - Question 2 - 2019 - Paper 2

Question 2

0.2.1 State what is meant by the internal energy of a gas. 0.2.2 Absolute zero of temperature can be interpreted in terms of the ideal gas laws or the kinetic energ... show full transcript

Worked Solution & Example Answer:0.2.1 State what is meant by the internal energy of a gas - AQA - A-Level Physics - Question 2 - 2019 - Paper 2

Step 1

State what is meant by the internal energy of a gas.

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Answer

The internal energy of a gas is the total sum of the kinetic and potential energies of the particles (atoms or molecules) that make up the gas. This includes the energy associated with the random motion of the particles, as well as any potential energy due to intermolecular forces.

Step 2

Absolute zero of temperature can be interpreted in terms of the ideal gas laws or the kinetic energy of particles in an ideal gas. Describe these two interpretations of absolute zero of temperature.

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Answer

Absolute zero is the temperature at which a gas would theoretically exert no pressure, according to the ideal gas law, stated as PV = nRT. If either the pressure (P) or volume (V) is zero, the temperature must be absolute zero.

In terms of kinetic energy, absolute zero is the temperature at which the average kinetic energy of the particles becomes zero. This implies that the particles are not moving at all, leading to a state where their energy is minimized.

Step 3

Calculate the root mean square speed (c_{rms}) of the argon atoms in the mixture.

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Answer

To calculate the root mean square speed of argon atoms, we use the formula: $c_{rms} = ext{sqrt} rac{3kT}{m}$ Where:

$k$ is the Boltzmann constant ( $1.38 imes 10^{-23} ext{ J K}^{-1}$ ),
$T = 310 ext{ K}$ ,
and $m$ is the mass of one argon atom.

First, we calculate the molar mass of argon in kg:

Molar mass of argon = $4.0 imes 10^{-2} ext{ kg mol}^{-1}$
$m = rac{4.0 imes 10^{-2}}{6.022 imes 10^{23}} = 6.64 imes 10^{-26} ext{ kg}$

Then substituting these values: $c_{rms} = ext{sqrt} rac{3 imes (1.38 imes 10^{-23}) imes 310}{6.64 imes 10^{-26}}$ Calculating gives: $c_{rms} ext{ is approximately } 440 ext{ m s}^{-1}$

Step 4

Compare the mean kinetic energy of the argon atoms and the helium atoms in the mixture.

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Answer

At a constant temperature, the mean kinetic energy of different gases is given by the equation: $KE_{avg} = rac{3}{2} k T$ This means both argon and helium atoms have the same average kinetic energy at 310 K, as they share the same temperature. However, due to their different molar masses, the distributions of speeds and therefore total kinetic energies may differ.

Step 5

Explain, in terms of the kinetic theory model, why a pressure is exerted by the gas on the piston.

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Answer

According to the kinetic theory of gases, the particles of a gas are in constant random motion and collide with the walls of the container (or piston). Each collision exerts a force on the wall, and when many particles collide, this results in a measurable pressure on the piston. The pressure can be defined as: $P = rac{F}{A}$ where $F$ is the total force exerted by the gas particles, and $A$ is the area of the piston.

Step 6

Explain, using the kinetic theory model, two changes that can be made independently to reduce the pressure exerted by the gas.

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Answer

Increase the volume of the cylinder: According to Boyle's law, increasing the volume while keeping the temperature constant will result in a decrease in pressure.
Decrease the temperature of the gas: Reducing the temperature decreases the average kinetic energy of the particles, which results in fewer and less forceful collisions with the piston, thereby reducing the pressure.

0.2.1 State what is meant by the internal energy of a gas - AQA - A-Level Physics - Question 2 - 2019 - Paper 2

Worked Solution & Example Answer:0.2.1 State what is meant by the internal energy of a gas - AQA - A-Level Physics - Question 2 - 2019 - Paper 2

State what is meant by the internal energy of a gas.

Absolute zero of temperature can be interpreted in terms of the ideal gas laws or the kinetic energy of particles in an ideal gas. Describe these two interpretations of absolute zero of temperature.

Calculate the root mean square speed (c_{rms}) of the argon atoms in the mixture.

Compare the mean kinetic energy of the argon atoms and the helium atoms in the mixture.

Explain, in terms of the kinetic theory model, why a pressure is exerted by the gas on the piston.

Explain, using the kinetic theory model, two changes that can be made independently to reduce the pressure exerted by the gas.

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