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Figure 4 shows a gas strut supporting the lid of a trailer - AQA - A-Level Physics - Question 3 - 2017 - Paper 6
Question 3
Figure 4 shows a gas strut supporting the lid of a trailer. A fixed mass of nitrogen gas is sealed into the cylinder of the strut. The gas is initially at a pressu... show full transcript
Worked Solution & Example Answer:Figure 4 shows a gas strut supporting the lid of a trailer - AQA - A-Level Physics - Question 3 - 2017 - Paper 6
Step 1
Calculate the pressure and temperature of the gas at the end of the compression assuming the compression to be an adiabatic process.
Answer
To find the final pressure and temperature of the gas, we can use the adiabatic process equations:
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For pressure, the relationship is given by: P_1 V_1^{eta} = P_2 V_2^{eta} where ( \beta = \gamma ) (adiabatic index) and ( V ) is volume.
Using the initial values: ( P_1 = 1.2 \times 10^6 \text{ Pa} ) ( V_1 = 9.0 \times 10^{-5} \text{ m}^3 ) ( V_2 = 6.8 \times 10^{-5} \text{ m}^3 )
Thus,
Solving this gives: ( P_2 \approx 1.8 \times 10^6 \text{ Pa} ).
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To find the final temperature, we use the formula:
Substituting in:
This yields: ( T_2 \approx 328 \text{ K} ).
Step 2
Explain why the rapid compression of the gas can be assumed to be an adiabatic process.
Answer
The rapid compression of the gas can be assumed to be adiabatic because during a fast process, there is insufficient time for heat transfer to occur between the gas and its surroundings. In an adiabatic process, the system is insulated, preventing any heat exchange, thus all the work done on the gas results in a change in internal energy and temperature without any heat loss.
Step 3
When the lid is closed slowly, the compression can be assumed to be isothermal.
Answer
In an isothermal process, the temperature of the gas remains constant. When the lid is closed slowly, the gas can exchange heat with its surroundings, allowing it to maintain the same temperature throughout the compression. Since pressure and volume change according to the ideal gas law, any work done on the gas is done at a consistent temperature, leading to different work done compared to an adiabatic process.
Step 4
Compare without calculation the work done in each process.
Answer
In an adiabatic process, the work done on the gas is higher due to the increased internal energy resulting from heat gain, as there is no heat loss. Conversely, in an isothermal process, the gas does work but the heat exchanged with the environment keeps its temperature constant, leading to less work done compared to the adiabatic case. Generally, the work done during an adiabatic compression exceeds that done during an isothermal compression due to the differences in temperature changes and heat management.