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 × 10⁻² kg mol⁻¹ c_{rms} = __________ 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 that make up the gas. It includes all the energy due to the random motion of atoms or molecules within the gas.

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.

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Answer

In the context of ideal gas laws, absolute zero is the temperature at which the volume of an ideal gas would theoretically become zero, implying that the gas exerts no pressure and occupies no space.
From a kinetic energy perspective, absolute zero corresponds to the state where the average kinetic energy of the particles in the gas is zero, meaning the particles have minimal motion.

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, we use the formula:

$c_{rms} = rac{ ext{sqrt}igg{(}3kT}{m}\bigg{)}$

where:

$k = 1.38 imes 10^{-23} ext{J K}^{-1}$ (Boltzmann's constant)
$T = 310 ext{K}$ (temperature)
$m = 4.0 imes 10^{-2} ext{kg mol}^{-1} = rac{4.0 imes 10^{-2}}{6.022 imes 10^{23}} ext{kg} = 6.64 imes 10^{-26} ext{kg}$ (mass of one argon atom).

Plugging in the values gives: $c_{rms} = ext{sqrt}igg{(} rac{3 imes (1.38 imes 10^{-23}) imes 310}{6.64 imes 10^{-26}}\bigg{)}$ $c_{rms} ext{= 440 m s}^{-1}$ .

Step 4

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

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Answer

At the same temperature, the mean kinetic energy of gas particles is directly proportional to the absolute temperature. Since both gases are at the same temperature, the mean kinetic energy will be the same for argon and helium.

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, gas pressure arises from the collisional impact of gas particles against the walls of the piston. When a gas particle collides with the piston, it exerts a force on the piston over a time interval which can be expressed using the formula $F = ext{change in momentum} / ext{change in time}$ . This continuous bombardment of particles generates a net force, hence exerting pressure.

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

Decrease the temperature of the gas. As temperature decreases, the kinetic energy of the gas particles also decreases, leading to fewer and less forceful collisions with the piston, which reduces pressure.
Increase the volume of the cylinder. By allowing more space for the gas particles, the frequency of collisions with the walls decreases, resulting in a reduction of the pressure exerted by the gas.

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.

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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