Respuesta :
Answer:
The final pressure of the gas when its temperature returns to its initial value [tex]1.8234\times 10^6[/tex] Pa.
Step-by-step explanation:
Given : An ideal gas is confined within a closed cylinder at a pressure of [tex]2.026\times 10^5[/tex] Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.
To find : What is the final pressure of the gas when its temperature returns to its initial value?
Solution :
Since the temperature is constant .
The relation between P and V is given by,
[tex]P_1\times V_1 = P_2\times V_2[/tex]
[tex]\frac{P_1}{P_2}=\frac{V_2}{V_1}[/tex] ....(1)
The piston moves until the volume of the gas is reduced to one-ninth of the initial volume i.e. [tex]V_2=\frac{V_1}{9}[/tex]
or [tex]\frac{V_2}{V_1}=\frac{1}{9}[/tex]
[tex]P_1=2.026\times 10^5[/tex]
Substitute in equation (1),
[tex]\frac{2.026\times 10^5}{P_2}=\frac{1}{9}[/tex]
[tex]P_2=9\times 2.026\times 10^5[/tex]
[tex]P_2=18.234\times 10^5[/tex]
[tex]P_2=1.8234\times 10^6[/tex]
The final pressure of the gas when its temperature returns to its initial value [tex]1.8234\times 10^6[/tex] Pa.
