9. small animals such as mice can live at reduced air pressures down to 20 kpa absolute (although not…

9. 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?

9. 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?

Answer

Explanation:

Step1: Convert manometer reading to kPa

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

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.