200 cc of air is kept at 760 mm of mercury pressure. Keeping the temperature constant, if the pressure on that air is increased by 1 mm of mercury, then its volume is decreased by 0.263 cc. Calculate the bulk modulus of air.

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Solution

Dear student

The bulk modulus of air is given by
$K = - V \frac{d P}{d V}$
where dP is the change in pressure and dV is the change in volume so
$K = - 200 c c \times \frac{1 m m}{- 0.263 c c}$
Since volume is not changed so much so we put V=200cc and volume is decreased so dV is negative hence
$K = \frac{200}{0.263} m m K = 760.45 m m K = 760.45 \times 133.322 P a K = 1.013 \times 10^{5} P a$

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