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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 , we can use the following equations for an adiabatic process:
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For pressure:
P_1 V_1^{eta} = P_2 V_2^{eta}
where eta = rac{C_p}{C_v} = γ = 1.4.
Substituting the values:
Solving this yields:
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For temperature, using the relation:
Substituting the values:
This simplifies to:
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 considered adiabatic because there is not enough time for heat transfer to occur between the gas and its surroundings. In such a short timeframe, any heat that might be lost or gained is negligible compared to the work done on the gas during compression.
Step 3
When the lid is closed slowly, the compression can be assumed to be isothermal.
Answer
In isothermal compression, the gas is allowed to exchange heat with its surroundings, keeping the temperature constant throughout the process. Since the initial and final states are the same, the work done can also be analyzed using the relationship:
where is the number of moles, is the gas constant, and and are the final and initial volumes, respectively. In comparison, since no heat transfer occurs in the adiabatic process, the work done will be larger due to the increase in internal energy.