Answer:
T₂= 226.21 K
Explanation:
Given that
At initial condition
P₁=2 atm
T₁=298 K
At final condition
P₂= 1 atm
Lets take final temperature = T₂
We know that specific heat ratio ,γ = 1.66
[tex]PV^{\gamma}=C[/tex]
P V = m RT
P=Pressure
V=Volume
m=Mass
R=gas constant
T=Temperature
[tex]T_1^{\gamma}P_1^{1-\gamma}=T_2^{\gamma}P_2^{1-\gamma}\\ T_2=T_1\times \left (\dfrac{P_2}{P_1} \right )^{\dfrac{\gamma-1}{\gamma}}[/tex]
[tex]T_2=298\times \left (\dfrac{1}{2} \right )^{\dfrac{1.66-1}{1.66}}[/tex]
[tex]T_2=226.21\ K[/tex]
Therefore the final temperature will be 226.21 K.
T₂= 226.21 K
