First slide

Different type of processes

Question

The pressure and density of a diatomic gas (γ = 7/5) change adiabatically from (P, d) to (P¹, d¹). If d¹/d = 32, then P¹/P should be

Easy

A

1/128
B

32
C

128
D

none of the above

Solution

$\gamma = \frac{7}{5}$
$\frac{{{d^1}}}{d} = 32,\,\,\frac{{{p^1}}}{p} = ?$
$p\alpha \frac{1}{{{V^\gamma }}} \Rightarrow V\alpha \frac{1}{d}$ $\therefore P\alpha {(d)^\gamma }$
$\frac{{{P^1}}}{P} = {\left( {\frac{{{d^1}}}{d}} \right)^\gamma } = {\left( {32} \right)^{7/5}} = {\left( {{2^5}} \right)^{7/5}} = {2^7} = 128$

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