(adsbygoogle = window.adsbygoogle || []).push({}); PROBLEM:

One mole of an ideal monatomic gas initially at 300 K (T_{1}) and a pressure of 15.0 atm (P_{1}) expands to a final pressure of 1.00 atm (P_{2}). The expansion occurs via an adiabatic and reversible path. Calculate q, w, ΔU, and ΔH.

SOLUTION:

q = 0 (adiabatic; no heat exchange occurs)

Thus, ΔU = w = C_{v}ΔT

ΔH = C_{p}ΔT

ΔT = T_{2}- T_{1}

Need T_{2}to calculate values (not an isothermal expansion)...

Known equation for reversible adiabatic process: P_{1}V_{1}^{γ}= P_{2}V_{2}^{γ}^{(γ = gamma)}

Using PV = nRT, substitute in and simplify to obtain expression for T_{2}...

T_{2}= T_{1}(P_{1}/P_{2})^{((1-γ)/γ)}

^{*where problems arise...}

γ = ?

The solutions manual says γ = 5/3, but I don't know how this value is obtained.

I do know that, as an ideal monatomic gas, the internal energy (U) of the gas (per mole?) is: 3/2RT (we assume only translations occur). But how is this related to C_{v}, C_{p}, and more importantly, γ?

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# Homework Help: Obtaining gamma (γ) in an adiabatic, reversible expansion

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