Question

1. small animals such as mice can live at reduced air pressures down to 20 kpa absolute (although not comfortably). in a test, a mercury manometer attached to a tank as shown in figure q9 reads 64.5 cm hg and the barometer reads 100 kpa. will the mice survive?

Explanation:

Step1: Convert manometer reading to kPa

We know that pressure due to a fluid column is $P =
ho gh$. The density of mercury $
ho_{Hg}=13595\ kg/m^{3}$, $g = 9.81\ m/s^{2}$, and $h = 64.5\ cm=0.645\ m$. So $P_{Hg}=
ho_{Hg}gh=13595\times9.81\times0.645\ Pa\approx86997\ Pa = 86.997\ kPa\approx87\ kPa$.

Step2: Calculate absolute pressure in the tank

The barometric pressure $P_{atm}=100\ kPa$. The pressure in the tank $P_{abs}$ is given by $P_{abs}=P_{atm}-P_{Hg}$. Substituting the values, we get $P_{abs}=100 - 87=13\ kPa$.

Answer:

No, the mice will not survive since the absolute pressure in the tank ($13\ kPa$) is less than the minimum pressure ($20\ kPa$) at which mice can live.