Answer :
Answer:
1.571 is the required ratio
Solution:
As per the question:
Pressure, P = [tex]1.50\times 10^{5}\ Pa[/tex]
Volume, V = [tex]0.08\ m^{3}[/tex]
Volume,V' = [tex]0.04\ m^{3}[/tex]
(a) To calculate the final pressure:
In adiabatic compression:
[tex]PV^{\gamma} = P'V'^{\gamma}[/tex]
[tex]\gamma = 1.67[/tex]
[tex]P' = (\frac{0.04}{0.08})^{1.67}\times 1.50\times 10^{5}[/tex]
[tex]P' = 4.713\times 10^{5}\ Pa[/tex]
(b) From the eqn of ideal gas:
PV = nRT
We can write:
[tex]\frac{P'V'}{PV} = \frac{T'}{T}[/tex]
where
T' = Final temperature
T = Initial temperature
Thus
[tex]\frac{4.713\times 10^{5}\times 0.04}{1.50\times 10^{5}\times 0.08} = \frac{T'}{T}[/tex]
[tex]\frac{T'}{T} = 1.571[/tex]