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Two gases X and Y kept in separate cylinders with same initial temperature and pressure are compressed to one third of their volume through isothermal and adiabatic process respectively. Which gas would have more pressure?
- a)Gas X has higher temperature
- b)Gas Y has higher pressure
- c)Gas Y has lower pressure
- d)Gas X and Y are at 0 atm pressure
Correct answer is option 'B'. Can you explain this answer?
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Two gases X and Y kept in separate cylinders with same initial tempera...
Work done in isothermal process is greater than work done in adiabatic process so Pressure of X is greater than Y.
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Two gases X and Y kept in separate cylinders with same initial tempera...
Answer:
The correct answer is (c) Gas Y has lower pressure.
Explanation:
Isothermal Compression:
When gas is compressed isothermally, the temperature remains constant throughout the process. The process takes place at a constant temperature, and the pressure and volume of the gas are inversely proportional to each other. In this case, gas X undergoes isothermal compression.
Adiabatic Compression:
When gas is compressed adiabatically, no heat exchange takes place between the gas and the surroundings. The process takes place at a constant rate, and the pressure and volume of the gas are inversely proportional to each other, but the temperature of the gas changes. In this case, gas Y undergoes adiabatic compression.
To find the final pressure of the gases, we can use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
For gas X:
Since the compression is isothermal, the temperature remains constant, and we can write:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume, respectively, and P2 and V2 are the final pressure and volume, respectively.
Therefore, P2 = (V1/V2)P1
Since V2 = (1/3)V1, we get:
P2 = 3P1
For gas Y:
Since the compression is adiabatic, we can use the adiabatic equation:
P1V1^γ = P2V2^γ
where γ is the ratio of specific heats, which is a constant for a given gas.
Therefore, P2 = P1(V1/V2)^γ
Since V2 = (1/3)V1, we get:
P2 = P1(3)^γ
Since γ > 1 for all gases, we have:
P2 < />
Therefore, gas Y has lower pressure than gas X after compression.
Conclusion:
Gas Y has a lower pressure than gas X after compression, even though they had the same initial temperature and pressure. The reason is that gas Y underwent adiabatic compression, which causes a greater decrease in volume and a greater increase in temperature, leading to a lower final pressure.
The correct answer is (c) Gas Y has lower pressure.
Explanation:
Isothermal Compression:
When gas is compressed isothermally, the temperature remains constant throughout the process. The process takes place at a constant temperature, and the pressure and volume of the gas are inversely proportional to each other. In this case, gas X undergoes isothermal compression.
Adiabatic Compression:
When gas is compressed adiabatically, no heat exchange takes place between the gas and the surroundings. The process takes place at a constant rate, and the pressure and volume of the gas are inversely proportional to each other, but the temperature of the gas changes. In this case, gas Y undergoes adiabatic compression.
To find the final pressure of the gases, we can use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
For gas X:
Since the compression is isothermal, the temperature remains constant, and we can write:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume, respectively, and P2 and V2 are the final pressure and volume, respectively.
Therefore, P2 = (V1/V2)P1
Since V2 = (1/3)V1, we get:
P2 = 3P1
For gas Y:
Since the compression is adiabatic, we can use the adiabatic equation:
P1V1^γ = P2V2^γ
where γ is the ratio of specific heats, which is a constant for a given gas.
Therefore, P2 = P1(V1/V2)^γ
Since V2 = (1/3)V1, we get:
P2 = P1(3)^γ
Since γ > 1 for all gases, we have:
P2 < />
Therefore, gas Y has lower pressure than gas X after compression.
Conclusion:
Gas Y has a lower pressure than gas X after compression, even though they had the same initial temperature and pressure. The reason is that gas Y underwent adiabatic compression, which causes a greater decrease in volume and a greater increase in temperature, leading to a lower final pressure.
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Two gases X and Y kept in separate cylinders with same initial tempera...
Work done in isothermal process is greater than work done in adiabativ process so P of X is greater than Y
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Two gases X and Y kept in separate cylinders with same initial temperature and pressure are compressed to one third of their volume through isothermal and adiabatic process respectively. Which gas would have more pressure?a)Gas X has higher temperatureb)Gas Y has higher pressurec)Gas Y has lower pressured)Gas X and Y are at 0 atm pressureCorrect answer is option 'B'. Can you explain this answer?
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