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Figure 5 shows a tool for driving nails into wood - AQA - A-Level Physics - Question 4 - 2021 - Paper 6
Question 4
Figure 5 shows a tool for driving nails into wood. Only part of the tool is shown. Fuel is mixed with air in the combustion chamber and is ignited by a spark. The g... show full transcript
Worked Solution & Example Answer:Figure 5 shows a tool for driving nails into wood - AQA - A-Level Physics - Question 4 - 2021 - Paper 6
Step 1
Deduce which nail in Table 2 is the correct one to use in the tool.
Answer
To determine the correct nail, we first need to calculate the work done by the expanding gas. The work done (W) by a gas can be represented by the formula:
Where:
- p is the pressure.
- ΔV is the change in volume.
From Figure 6, we need to estimate the pressure at various volumes, particularly for the range from 20 × 10^-6 m³ to 80 × 10^-6 m³. This will help us determine the average pressure.
Next, we calculate the change in volume:
Next, we can estimate average pressure from the graph by taking two points within our volume range. For example, at about 20 × 10^-6 m³, the pressure is approximately 10 × 10^5 Pa, and at around 60 × 10^-6 m³, the pressure might be about 4 × 10^5 Pa.
The average pressure (p_avg) can be estimated as:
p_{avg} = rac{(10 + 4) imes 10^5}{2} = 7 imes 10^5 Pa
Now, substituting the pressure and change in volume into the work done formula:
To drive a nail completely, we look at Table 2 across the various nails. We find the corresponding forces and lengths:
- Nail A requires 250 N.
- Nail B requires 320 N.
- Nail C requires 370 N.
- Nail D requires 420 N.
- Nail E requires 560 N.
The force can be related by:
Given the work done is around 28 J, and using each force from Table 2, we calculate:
- For Nail A:
- For Nail B:
- For Nail C:
- For Nail D:
- For Nail E:
From these calculations, we see that Nail D, requiring 21 J, is the closest within the work calculated of around 28 J, making it the correct option.
Step 2
Discuss why the expansion cannot be isothermal.
Answer
The expansion in the tool cannot be isothermal for the following reasons:
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Rapid Expansion: The gas expands rapidly when ignited, which means there isn’t enough time for thermal equilibrium to be achieved. An isothermal process requires the system to remain in thermal contact with its surroundings, allowing it to exchange heat. In this case, the rapid motion of the gases does not allow heat exchange to maintain a constant temperature.
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Combustion Reaction: The ignition of fuel generates significant heat. During the expansion, the temperature of the gas would actually increase due to the combustion process, which contrasts with the isothermal condition where temperature is constant.
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Piston Dynamics: The piston drives the nail into the wood and the high-speed movements further indicate that the gas is effectively doing work rapidly, which also leads to cooling and heating effects that deviate from the isothermal assumptions.
Thus, due to the nature of rapid gas expansion, combustion heating, and piston dynamics, the expansion process is significantly different from an isothermal process.