A helium-filled balloon escapes a child's hand at sea level and 20.1 ∘C. Part A When it reaches an altitude of 3600 m, where the temperature is 5.9 ∘C and the pressure is only 0.72 atm , how will its volume compare to that at sea level?

The volume of the helium-filled balloon would have increased by 1.46 times.

From the gas law:

                         P1V1/T1 = P2V2/T2

P1V1T2 = P2V2T1

Hence; V2/V1 = P1T2/P2T1

In this case, P1 = pressure at sea level = 1 atm, P2 = 0.72 atm, T1 = 20.1 = 293.1, and T2 = 5.9 = 278.9

V2/V1 = 1 x 293.1/0.72 x 278.9

              = 1.46

Therefore, V2 = 1.46V1

The volume of the balloon will have increased by 1.46x.

More on the gas law can be found here: link

The volume at an altitude of 3600m will be 1.320 times the volume at sea level.

Explanation:

PV/T=CONSTANT

V2/V1=(P1/P2)×(T2/T1)

V2/V1 = (1 / 0.72) × (5.9+273.15 / 20.1+273.15)

          = (1 / 0.72) × (279.05 / 293.25)

          = 1.389 × 0.951

V2 / V1 = 1.320

V2 = 1.320 V1

V1 = volume at sea level

V2 = volume at 3600m

a mercury barometer is a device that uses the physical properties of mercury in a tube to measure barometric pressure. mercury barometers are used for : -

1. measurement of atmospheric pressure  

2. determining the altitude of a place

3. weather forecasting

4. calibration and checking of aneroid barometers

5. application in fluid mechanics

6. measurement of pressure in aircrafts

7. surface weather analysis

8. preparation of barographs

9. usage in physical sciences like physics, astronomy & chemistry

10. preparation of aircraft altimeters

characteristics of mercury barometer : -

1.used to define and measure atmospheric pressure.

2.on the average at sea level the column of mercury rises to a height of about 760 mm.

3.this quantity is equal to 1 atmosphere.

4.it is also known as standard atmospheric pressure.

5.a barometer in which the weight of a column of mercury in a glass tube with a sealed top is balanced against that of the atmosphere pressing on an exposed cistern of mercury at the base of the mercury column, the height of the column varying with atmospheric pressure.