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## Homework Statement:

- A recipient with a plunger/piston is filled with Helium. The gas has initial temperature T1, pressure P and occupies a volume V1. Suddenly, the pressure changes to P/5 and the Helium expands irreversibly while heating up to T2. Find the internal energy change, the work realized during the expansion and the heat exchanged during the process.

## Relevant Equations:

- Thermodynamics equations

According to the first principle of thermodynamics: ΔU = W + Q

Also noting that: W = -P⋅ΔV (Question: This P is the initial pressure or the final?)

To find V2:

(P1⋅V1) / T1 = (P2⋅V2) / T2 → Therefore, (P⋅V1) / T1 = [(P/5)⋅V2] / T2 → (P⋅V1) / T1 = (P⋅V2) / (5⋅T2) →

So, ΔV = V2 - V1 = [(5⋅T2⋅V1) / T1] - T1 →

Now, to replace in the formula of the work

And also, it is OK to use Q = T2-T1 ?

Also noting that: W = -P⋅ΔV (Question: This P is the initial pressure or the final?)

To find V2:

(P1⋅V1) / T1 = (P2⋅V2) / T2 → Therefore, (P⋅V1) / T1 = [(P/5)⋅V2] / T2 → (P⋅V1) / T1 = (P⋅V2) / (5⋅T2) →

**V2 = (5⋅T2⋅V1) / T1**So, ΔV = V2 - V1 = [(5⋅T2⋅V1) / T1] - T1 →

**ΔV = [V1(5⋅T2 - T1)] / T1**Now, to replace in the formula of the work

**W = -P⋅ΔV**do I use P or P/5 ?And also, it is OK to use Q = T2-T1 ?