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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.
Answer
The internal energy of a gas is defined as the sum of the kinetic and potential energies of all the particles (atoms/molecules) in the gas. It takes into account both random motions (kinetic) and intermolecular interactions (potential) that contribute to the total energy of the system.
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.
Answer
In terms of the ideal gas laws, absolute zero (0 K) is the theoretical temperature at which the volume of an ideal gas would approach zero, since the pressure and volume are directly related (Boyle's Law).
From the kinetic theory perspective, absolute zero is the temperature at which the kinetic energy of particles is zero, implying that the particles are at rest with no motion.
Step 3
Calculate the root mean square speed (c_{rms}) of the argon atoms in the mixture.
Answer
The root mean square speed () can be calculated using the formula:
c_{rms} = rac{ ext{sqrt}(3RT)}{M}
where:
- = gas constant (8.314 J/(mol·K))
- = temperature in Kelvin (310 K)
- = molar mass in kg/mol (for argon, )
Substituting the values, we get:
= 440 ext{ m/s}$$Step 4
Compare the mean kinetic energy of the argon atoms and the helium atoms in the mixture.
Answer
At the same temperature, the mean kinetic energy for both gases can be described using the formula:
KE = rac{3}{2}kT
where is the Boltzmann constant. Since both gases are at the same temperature, their mean kinetic energies will be equal, meaning that the argon and helium atoms have the same average kinetic energy when in equilibrium.
Step 5
Explain, in terms of the kinetic theory model, why a pressure is exerted by the gas on the piston.
Answer
According to the kinetic theory model, gas molecules are in constant random motion and collide with surfaces, including the walls of the piston. Each collision exerts a force, and the cumulative effect of a large number of collisions produces pressure. The pressure on the piston results from the change in momentum of the molecules during these collisions.
Step 6
Explain, using the kinetic theory model, two changes that can be made independently to reduce the pressure exerted by the gas.
Answer
-
Reducing the temperature of the gas decreases the average kinetic energy of the particles, resulting in fewer and less forceful collisions with the piston walls, thus reducing pressure.
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Increasing the volume of the cylinder allows more space for the gas particles to move; as they have more space, the frequency of collisions with the piston decreases, which also reduces the pressure.