Answer:
v₁ = 4 [m/s].
Explanation:
This problem can be solved by using the principle of conservation of linear momentum. Where momentum is preserved before and after the missile is fired.

where:
P = linear momentum [kg*m/s]
m = mass [kg]
v = velocity [m/s]

where:
m₁ = mass of the tank = 500 [kg]
v₁ = velocity of the tank after firing the missile [m/s]
m₂ = mass of the missile = 20 [kg]
v₂ = velocity of the missile after firing = 100 [m/s]
![(500*v_{1})=(20*100)\\v_{1}=2000/500\\v_{1}=4[m/s]](https://tex.z-dn.net/?f=%28500%2Av_%7B1%7D%29%3D%2820%2A100%29%5C%5Cv_%7B1%7D%3D2000%2F500%5C%5Cv_%7B1%7D%3D4%5Bm%2Fs%5D)
Answer:

Explanation:
An adiabatic process refers to one where there is no exchange of heat.
The equation of state of an adiabatic process is given by,

where,
= pressure
= volume

= constant
Therefore, work done by the gas during expansion is,



(using
)

Answer:149.73 ml
Explanation:
Given

change in volume is given by

![\Delta V=\nu_{initial}\beta _{acetone}\left [ T_f-T_i\right ]](https://tex.z-dn.net/?f=%5CDelta%20V%3D%5Cnu_%7Binitial%7D%5Cbeta%20_%7Bacetone%7D%5Cleft%20%5B%20T_f-T_i%5Cright%20%5D)
![V_{final}=\nu_{initial}+\nu_{initial}\beta _{acetone}\left [ T_f-T_i\right ]](https://tex.z-dn.net/?f=V_%7Bfinal%7D%3D%5Cnu_%7Binitial%7D%2B%5Cnu_%7Binitial%7D%5Cbeta%20_%7Bacetone%7D%5Cleft%20%5B%20T_f-T_i%5Cright%20%5D)
![V_{final}=150+150\times 1.50\times 10^{-4}\left [ 20-32\right ]](https://tex.z-dn.net/?f=V_%7Bfinal%7D%3D150%2B150%5Ctimes%201.50%5Ctimes%2010%5E%7B-4%7D%5Cleft%20%5B%2020-32%5Cright%20%5D)

Calculating the average speed is simple using the formula <span>speed = distance/time</span>