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Semenov [28]
3 years ago
7

At the end of the adiabatic expansion, the gas fills a new volume V₁, where V₁ > V₀. Find W, the work done by the gas on the

container during the expansion. Express the work in terms of p₀, V₀, and V₁. Your answer should not depend on temperature.
Physics
1 answer:
tino4ka555 [31]3 years ago
4 0

Answer:

W=\frac{p_0V_0-p_1V_1}{\gamma-1}

Explanation:

An adiabatic process refers to one where there is no exchange of heat.

The equation of state of an adiabatic process is given by,

pV^{\gamma}=k

where,

p = pressure

V = volume

\gamma=\frac{C_p}{C_V}

k = constant

Therefore, work done by the gas during expansion is,

W=\int\limits^{V_1}_{V_0} {p} \, dV

=k\int\limits^{V_1}_{V_0} {V^{-\gamma}} \, dV

=\frac{k}{\gamma -1} (V_0^{1-\gamma}-V_1^{1-\gamma})\\

(using pV^{\gamma}=k )

=\frac{p_0V_0-p_1V_1}{\gamma-1}

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