Answer:
Volume = 90 cm³
Step-by-step explanation:
Given:
The volume 'V' of a fixed amount of gas is directly proportional to the temperature 'T' and inversely proportional to the pressure 'P'.
Initial volume is, [tex]V_1=160\ cm^3[/tex]
Initial temperature is, [tex]T_1=320\ K[/tex]
Initial pressure is, [tex]P_1=12\ kg/cm^2[/tex]
Final temperature is, [tex]T_2=240\ K[/tex]
Final pressure is, [tex]P_2=16\ kg/cm^2[/tex]
Final volume is, [tex]V_2=?[/tex]
As per question:
[tex]V\propto\frac{T}{P}[/tex]
Therefore,
[tex]\frac{PV}{T}=Constant[/tex]
Or, we can write the above as:
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\\\\\frac{12\times 160}{320}=\frac{16\times V_1}{240}\\\\6=\frac{V_1}{15}\\\\V_1=15\times 6=90\ cm^3[/tex]
Therefore, the final volume is 90 cm³.
