213k views
2 votes
What happens to the air pressure inside a balloon when it is squeezed to half its volume at constant temperature? What happens to the air pressure inside a balloon when it is squeezed to half its volume at constant temperature? It is cut in half. It doubles. It quadruples. It remains the same.

User Ameet
by
8.2k points

1 Answer

2 votes

Answer:

The correct option is option (B)

Therefore the air pressure inside the balloon will be double.

Step-by-step explanation:

Boyle's Law:

At a constant temperature, the pressure of a given mass of an ideal gas varies inversely to its volume.


P\propto \frac1 V

Charles Law:

At a constant pressure, the volume of a given mass of an ideal gas varies directly to its temperature (in kelvin).


V\propto T

Combination of two laws is


(PV)/(T)=constant

Then,


(P_1V_1)/(T_1)=(P_2V_2)/(T_2)

Given that,

The final volume is half of initial volume and the temperature remains constant.

So,
T_1=T_2,
V_2=\frac12 V_1

Then,


(P_1V_1)/(T_1)=(P_2V_2)/(T_2)


\Rightarrow (P_1V_1)/(T_1)=(P_2.\frac12 V_1)/(T_1)


\Rightarrow P_1=\frac12 P_2


\Rightarrow P_2= 2P_1

⇒Final Pressure = twice of the initial pressure

Therefore the air pressure inside the balloon will be double.

User Kyanro
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.