Question

(a) It is known that density ρ of air decreases with height y as

Where = 1.25 kg m–3 is the density at sea level, and y0 is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value of gremains constant.

(b) A large He balloon of volume 1425 m3 is used to lift a payload of 400 kg. Assume that the balloon maintains constant radius as it rises. How high does it rise?

[Take y0= 8000 m and = 0.18 kg m–3].

Answer 1

Question 10.1:Exp

lain why
(a)
The blood pressure in humans is greater at the feet than at the brain
(b)
Atmospheric pressure at a height of about 6 km decreases to nearly half of itsvalue at the sea level, though the height of the atmosphere is more than 100 km
(c)
Hydrostatic pressure is a scalar quantity even though pressure is force divided byarea.ANS:
(a)
The pressure of a liquid is given by the relation:
P
=
hρ
gWhere,
P
= Pressure
h
= Height of the liquid column
ρ
= Density of the liquidg = Acceleration due to the gravityIt can be inferred that pressure is directly proportional to height. Hence,the bloodpressure in human vessels depends on the height of the blood column in the body.The height of the blood column is more at the feet than it is at the brain. Hence, theblood pressure at the feet is more than it is at the brain.
(b)
Density of air is the maximum near the sea level. Density of air decreases withincrease in height from the surface. At a height of about 6 km, density decreases tonearly half of its value at the sea level. Atmospheric pressure is proportional todensity. Hence, at a height of 6 km from the surface, it decreases to nearly half of itsvalue at the sea level.