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A quantity of monatomic ideal gas expands adiabatically from a volume of 2.0 liters to 6.0 liters. if the initial pressure is p0, what is the final pressure?

User Bobwki
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1 Answer

3 votes

Answer:

1/3p0

Step-by-step explanation:

The combined gas law:

P1V1/T1 = P2V2/T2, where P, V and T are Pressure, Volume, and Temperature. Temperature must always be in Kelvin. The subscriopts 1 and 2 are for initial (1) and final (2) conditions.

In this case, temperature is constant (adiabatically). V1 = 2.0L and V2 = 6.0L. I'll assume P1 = p0.

Rearrange the combined gas law to solve for final pressure, P2:

P1V1/T1 = P2V2/T2

P2 = P1*(V1/V2)*(T2/T1) [Note how I've arranged the volume and temoperature terms - as ratios. This helps us understand what the impact of raising or lowering one on the variables will do to the system].

No enter the data:

P2 = P1*(V1/V2)*(T2/T1): [Since T2 = T1, the (T2/T1) terms cancels to 1.]

P2 = p0*(2.0L/6.0L)*(1)

P2 = (1/3)p0

The final pressure is 1/3 the initial pressure.

User ALL
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