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Ideal Gas Equation

A mass of gas...

Question

A mass of gas is compressed in a quasi-static process from $80 k P a$ , $0.1 m^{3} t o 0.4 M P a, 0.03 m^{3}$ . Assuming that the pressure and volume are related by $P V^{n} = constant$ . The work done by the gas system is

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Solution

$P V^{n} = constant$

$P_{1} V_{1}^{n} = P_{2} V_{2}^{n}$

$80 \times (0.1)^{n} = 400 \times (0.03)^{n}$

$∴ n = 1.34$

$W = \frac{P_{1} V_{1} - P_{2} V_{2}}{n - 1}$

$= \frac{80 \times 0.1 - 400 \times 0.03}{1.34 - 1} = - 11.8 k J$

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