Respuesta :
Answer:
The correct option is option (B)
Therefore the air pressure inside the balloon will be double.
Explanation:
Boyle's Law:
At a constant temperature, the pressure of a given mass of an ideal gas varies inversely to its volume.
[tex]P\propto \frac1 V[/tex]
Charles Law:
At a constant pressure, the volume of a given mass of an ideal gas varies directly to its temperature (in kelvin).
[tex]V\propto T[/tex]
Combination of two laws is
[tex]\frac{PV}{T}=constant[/tex]
Then,
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
Given that,
The final volume is half of initial volume and the temperature remains constant.
So, [tex]T_1=T_2[/tex], [tex]V_2=\frac12 V_1[/tex]
Then,
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
[tex]\Rightarrow \frac{P_1V_1}{T_1}=\frac{P_2.\frac12 V_1}{T_1}[/tex]
[tex]\Rightarrow P_1=\frac12 P_2[/tex]
[tex]\Rightarrow P_2= 2P_1[/tex]
⇒Final Pressure = twice of the initial pressure
Therefore the air pressure inside the balloon will be double.
