Question

During a flight, a scientist was supposed to take his instruments on plane so he had to put them all in an extremely fastened cylindrical bag. Initially the bag was 10 cm in diameter and 20 cm in length and the filled air inside it had a mass of 100 grams. During this flight, the pressure inside the plane was dropped to 0.8 of the initial pressure while the temperature remained constant at 20 ֯ C. Determine
a) The volume of the bag.
b) If the molar mass of the air is 29 grams/mole. How many moles of air is inside the bag.
c) Is the bag volume is expected to increase or decrease in the bag? By what factor if so and determine the new volume. Explain.
d) The speed of the air molecules in the bag before and after being on the plane.
e) The total internal energy of the gas molecules before and after be- ing on the plane.
f) Now to control the volume of the bag, the scientist pressed firmly on the bag doing 20 J of work on the air, while the air temperature increased by 5 ֯C. Determine the heat flow to or from the gas?

Answer 1

a)

volume of cylinder == 1570.79 .ml

b)

n= 100/29= 3.44

c) the bag is expected to increase in volume

mass of air = 100g

density of air =1.2041 g/ml

so volume of air in it = 120.41 ml

now when the pressure drops to 0.8

using PV= constant

we get

new volume of bag = 1570+30.1 =1600.81 ml

d) the speed does not change since the temperature is constant

e) the knietic energy also remains same

f)

let us assume the gas to diatomic (normal air is mostly diatomic)

now change in inetrnal energy due to the 5 degree rise =

= 3.44X 2.5 X 8.314 X 5= 357.502 J

work done = 20 J

Heat out of the gas = = 337.5 J