Consider a balloon that has a volume v it contains in moles of gas it has internal pressure of p its temperature is t if the balloon is heated to a temperature of 15.5 t well it is placed under high-pressure of 15.5 p how does the volume of the balloon change

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Volume does not change.

Explanation:-

Initial Pressure P 1 = P

Initial Temperature T 1 = T

Initial Volume V 1 = V

New Pressure P 2 = 15.5 P

New Temperature T 2 = 15.5 T

Using the relation

P 1 V 1 / T 1 = P2 V2 / T2

V 2 = P 1 V 1 T 2 / (T 1 P 2)

= P x V x 15.5 T / ( T x 15.5 P)

= V

We see the new volume is same as initial volume.

So the volume does not change.

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