Question

A glass tumbler containing $243mL$ of air at $100kPa$ and ${20}^{\circ }C$ is turned upside down and immersed in a water bath to a depth of $20.5metre$. The air in the glass is compressed by the weight of water above it. Calculate the volume of air in the glass assuming the temperature and the barometric pressure have not changed.

Answer 1

Hydrostatic pressure $=h\times d\times g$
$=20.5\times 1\times 9.81$
$=201.105kPa$
Inside the water both atmospheric pressure and hydro static pressure acts, therefore
$P_{total}=100+201.105=301.105kPa$
Applying boyle's law,

$P_1{V}_1=P_2{V}_2$
$100\times 243=301.105\times V_2$
$V_2=80.70mL$.