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A container of volume 1 m3 is divided into two equal parts by a partition. One part has an ideal gas at 300 K and the other part is vacuum. The whole system is thermally isolated from the surroundings. When the partition is removed, the gas expands to occupy the whole volume. Its temperature will now be ____ .
Correct answer is '0'. Can you explain this answer?
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A container of volume 1 m3 is divided into two equal parts by a partit...
Since . the system is insulated 0 = 0. Other part is vacuum . therefore , work done by the gas W ia also zero. Hence . from first law o f thermodynamics , ΔU = 0 i.e. temperature remains constant.
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A container of volume 1 m3 is divided into two equal parts by a partit...
Explanation:
The given scenario can be understood using the concept of adiabatic expansion.
Adiabatic Expansion:
- Adiabatic process occurs without the transfer of heat between the system and its surroundings.
- In this case, when the partition is removed, the gas expands into the vacuum side adiabatically.
Key Points:
- The initial volume of the gas is 0.5 m3 (half of the total volume).
- The final volume of the gas is 1 m3 (whole volume).
- Since the process is adiabatic, the expansion is reversible.
- Since no heat exchange occurs, the internal energy of the gas remains constant.
Temperature Change:
- For an adiabatic expansion, the equation relating initial and final temperatures and volumes is T1V1^(γ-1) = T2V2^(γ-1), where γ is the ratio of specific heats.
- Since the initial volume is half the final volume, and the gas expands into vacuum, the final volume is occupied by the gas only.
- This results in V1 = V2 and T1 = T2, leading to T2 = T1 = 300 K.
Therefore, the temperature of the gas after expansion will be 300 K, the same as the initial temperature. This is because the process is adiabatic and the internal energy of the gas remains constant, resulting in no temperature change.
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A container of volume 1 m3 is divided into two equal parts by a partition. One part has an ideal gas at 300 K and the other part is vacuum. The whole system is thermally isolated from the surroundings. When the partition is removed, the gas expands to occupy the whole volume. Its temperature will now be ____ .Correct answer is '0'. Can you explain this answer?
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