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Chapter 28: Q. 48 (page 792)

The circuit shown in FIGURE P28.48 is inside a 15cmdiameter balloon filled with helium that is kept at a constant pressure of 12atm. How long will it take the balloon’s diameter to increase to 16 cm?

Short Answer

Expert verified

Time taken is16s.

Step by step solution

01

Given information

We have given,

Diameter of the balloon =15cm

Pressure =1.2atm

We have to find the time taken by the balloon to change its diameter to16cm.

02

Simplify

The equivalent resistance of resistances in parallel as shown in the figure

1Req1=1R1+1R21Req1=1200+1300=5600Req1=120Ω

Then the total resistance of the circuit will be

Req=120+280=400Ω

The total power dissipated by the circuit

P=V2R=(45)2400=5.06

then heat will be generated as

H=PtH=5t

We know from the law of thermodynamics

localid="1649414991464" H=32nRT=5t5t=32P(V2-V1)

Then,

V1-V2=4π((0.16)2-(0.15)2)3V1-V2=0.14×10-3m3t=3×12×0.14×10-310t=16s

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