A number of assumptions are made when explaining the behaviour of a gas using the molecular kinetic theory model. State one assumption about the size of molecules. At A the temperature of the gas is 27 °C. The gas then undergoes two changes, one from A to B and then one from B to C. Figure 1 shows how the pressure changes with volume for a fixed mass of an ideal gas. Calculate the number of gas molecules trapped in the cylinder using information from the initial situation at A. Calculate, in K, the change in temperature of the gas during the compression that occurs between A and B. Deduce whether the temperature of the gas changes during the compression from B to C. Compare the work done on the gas during the change from A to B with that from B to C on Figure 1.

A-Level AQA Physics Ideal Gases: A number of assumptions are made

A number of assumptions are made when explaining the behaviour of a gas using the molecular kinetic theory model - AQA - A-Level Physics - Question 1 - 2017 - Paper 2

Question 1

A number of assumptions are made when explaining the behaviour of a gas using the molecular kinetic theory model. State one assumption about the size of molecules. ... show full transcript

Worked Solution & Example Answer:A number of assumptions are made when explaining the behaviour of a gas using the molecular kinetic theory model - AQA - A-Level Physics - Question 1 - 2017 - Paper 2

Step 1

State one assumption about the size of molecules.

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Answer

The volume or size of the gas molecules is negligible when compared to the volume of the gas that they occupy.

Step 2

Calculate the number of gas molecules trapped in the cylinder using information from the initial situation at A.

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Answer

Using the ideal gas equation, we have:

$N = \frac{P V}{k T}$

Where:

P = 1.0 × 10^5 Pa
V = 0.50 × 10^{-3} m³
k = 1.38 × 10^{-23} J/K (Boltzmann constant)
T = 300 K (27 °C in Kelvin)

Calculating:

$N = \frac{(1.0 × 10^5) (0.50 × 10^{-3})}{1.38 × 10^{-23} (300)} ≈ 1.17 × 10^{20} \text{ molecules}$

Step 3

Calculate, in K, the change in temperature of the gas during the compression that occurs between A and B.

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Answer

The pressures and volumes for states A and B can be obtained from Figure 1. Assuming:

At A: $P_A = 1 \times 10^5 \text{ Pa}, V_A = 0.50 \times 10^{-3} \text{ m}^3$
At B: $P_B = 2 \times 10^5 \text{ Pa}, V_B = 0.30 \times 10^{-3} \text{ m}^3$

Using the relationship defined by the ideal gas law and manipulating it we find:

$T_B = \frac{P_B V_B}{k N}$

Thus, calculating the temperatures gives us:

$T_A = 300 K, T_B ≈ 215 K$

Therefore, the change in temperature is:

$ΔT = T_B - T_A = 215 - 300 = -85 K$

Step 4

Deduce whether the temperature of the gas changes during the compression from B to C.

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Answer

The temperature of the gas does change from B to C. Given that the pressure at B is higher than at A, and if we deduce from gas laws that volume is inversely proportional to pressure under constant mass, it can be inferred that the temperature will not remain constant and will likely decrease further.

Step 5

Compare the work done on the gas during the change from A to B with that from B to C on Figure 1.

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Answer

The work done on the gas can be determined using the area under the curves in Figure 1. For the transformation from A to B:

$W_{AB} = \text{Area under AB curve}$

And for B to C:

$W_{BC} = \text{Area under BC curve}$

Since the area under the curve represents the work done, quantitatively comparing these two areas will show that the work done on the gas during the compression from A to B is greater than the work done during B to C due to how pressure changes while volume changes.

A number of assumptions are made when explaining the behaviour of a gas using the molecular kinetic theory model - AQA - A-Level Physics - Question 1 - 2017 - Paper 2

Worked Solution & Example Answer:A number of assumptions are made when explaining the behaviour of a gas using the molecular kinetic theory model - AQA - A-Level Physics - Question 1 - 2017 - Paper 2

State one assumption about the size of molecules.

Calculate the number of gas molecules trapped in the cylinder using information from the initial situation at A.

Calculate, in K, the change in temperature of the gas during the compression that occurs between A and B.

Deduce whether the temperature of the gas changes during the compression from B to C.

Compare the work done on the gas during the change from A to B with that from B to C on Figure 1.

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