Chapter 28: Q. 48 (page 792)

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

Short Answer

Expert verified

Time taken is $16 s .$

Step by step solution

Given information

We have given,

Diameter of the balloon = $15 cm$

Pressure = $1.2 atm$

We have to find the time taken by the balloon to change its diameter to $16 cm .$

Simplify

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

$\frac{1}{R_{eq 1}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \frac{1}{R_{e q 1}} = \frac{1}{200} + \frac{1}{300} = \frac{5}{600} R_{e q 1} = 120 Ω$

Then the total resistance of the circuit will be

$R_{eq} = 120 + 280 = 400 Ω$

The total power dissipated by the circuit

$P = \frac{V^{2}}{R} = \frac{{(45)}^{2}}{400} = 5.06$

then heat will be generated as

$H = Pt H = 5 t$

We know from the law of thermodynamics

localid="1649414991464" $H = \frac{3}{2} nRT = 5 t 5 t = \frac{3}{2} P (V_{2} - V_{1})$

Then,

$V_{1} - V_{2} = \frac{4 π ({(0.16)}^{2} - {(0.15)}^{2})}{3} V_{1} - V_{2} = 0.14 \times 10^{- 3} m^{3} t = \frac{3 \times 12 \times 0.14 \times 10^{- 3}}{10} t = 16 s$

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

Short Answer

Step by step solution

Given information

Simplify

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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

Step by step solution

Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Electricity and Magnetism

Rotational Dynamics

Electromagnetism

Energy Physics

Medical Physics

Study anywhere. Anytime. Across all devices.

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