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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 after the adiabatic compression, we use the formulas related to adiabatic processes:
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For an adiabatic process, the relationship among pressure (P), volume (V), and temperature (T) can be expressed as:
P_1 V_1^{eta} = P_2 V_2^{eta}
where ( \beta = \gamma = 1.4 ) for nitrogen.
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Substituting given values:
Solving for ( P_2 ), we find:
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To find the final temperature ( T_2 ), we use the formula:
Substituting the values:
Solving this gives:
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 an adiabatic process for the following reasons:
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No Heat Transfer: In an adiabatic process, there is no significant heat transfer between the system and its surroundings. Given that the compression occurs quickly, there is insufficient time for heat exchange to take place. Thus, the entire process maintains the internal energy within the gas.
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Speed of Compression: Since the compression is rapid, it does not allow the gas to reach thermal equilibrium with its environment. Thus, heat is not added or removed from the gas, fulfilling the criteria for an adiabatic process.
Step 3
When the lid is closed slowly, the compression can be assumed to be isothermal.
Answer
During slow compression, the temperature of the gas remains relatively constant due to heat transfer. This can be understood through the following points:
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Heat Exchange: In this scenario, the gas can exchange heat with its surroundings. This heat exchange allows the gas to maintain a constant temperature, hence the term 'isothermal'.
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Equal Volume Changes: As the volume of the gas changes, it absorbs heat to counterbalance the work done on it. Consequently, the internal energy remains constant, aligning with the characteristics of an isothermal process.
Step 4
Compare without calculation the work done in each process.
Answer
In comparing the work done during adiabatic and isothermal processes under the same initial and final states:
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Work Done in Adiabatic Process: The work done during an adiabatic process is generally less than that during an isothermal process for the same change in volume because no heat is transferred to maintain the temperature. The gas's internal energy decreases significantly, leading to a relatively smaller amount of work done.
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Work Done in Isothermal Process: In contrast, the isothermal compression allows heat to enter the system, resulting in greater work done on the gas. This heat input compensates for the work required to compress the gas.
Overall, the amount of work done in the isothermal process is greater compared to the adiabatic process for the same change in volume due to the heat transfer involved.