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First Law of Thermodynamics & Ideal Gas Law

热力学第一定律与理想气体状态方程

ΔU=Q+W,T1​P1​V1​​=T2​P2​V2​​

Theoretical Identity Description:

Conservation of energy for thermal systems: internal energy change (ΔU) equals heat absorbed (Q) plus work done ON the system (W). For ideal gases, PV/T is invariant.

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Rigorous Derivation Tree

2 Logical Steps
Step 1check_circleValid Deduction
ΔU=Q+W,T1​P1​V1​​=T2​P2​V2​​

Foundational identity statement defined under standard mathematical conditions.

Step 2check_circleValid Deduction
ΔU=Q+W,TPV​=const

Targeted algebraic evaluation and parameter substitution.

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CSCA Exam Triggers & Traps

High-Yield Exam Focus
psychologyProblem Pattern Recognition

Use for isothermal (T=const), isobaric (P=const), isochoric (V=const), and adiabatic (Q=0) cylinder piston processes.

errorCommon Examination Pitfalls

Gas expansion does work ON the surroundings (W < 0). Gas compression receives work FROM the surroundings (W > 0).

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