A monoatomic gas (γ=5/3) is suddenly compressed to 1/8 of its original volume adiabatically, then the pressure of the gas will change to:
Correct answer: D. 32 times its initial pressure
- A. 24/5
- B. 40/3
- C. 8
- D. 32 times its initial pressure
Explanation
In an adiabatic process for a monoatomic gas, the relation PVγ = constant applies, where γ (gamma) is the adiabatic index, which is 5/3 for a monoatomic gas. Given that the volume is compressed to 1/8 of its original value, the pressure must increase to maintain the constant value of PVγ. This yields a pressure increase by a factor of 32. Therefore, the correct answer is that the pressure becomes 32 times its initial value. The other options result from incorrect calculations or misunderstandings of the adiabatic process formula.
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About First Law of Thermodynamics
The first law relates heat supplied, work done and the change in internal energy through energy conservation. Problems use sign conventions and apply the law to isothermal, adiabatic, isobaric and isochoric processes. Internal energy is a state function, while heat and work depend on the path followed.
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