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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鈥檚 diameter to increase to 16 cm?

Short Answer

Expert verified

Time taken is $16 s .$

Step by step solution

01

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 $16 cm .$

02

Simplify

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

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

Then the total resistance of the circuit will be

$R_{eq} = 120 + 280 = 400 鈩�$

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,

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

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Most popular questions from this chapter

Rank in order, from largest to smallest, the powers $P_{a}$ to $P_{d}$ dissipated by the four resistors in FIGURE

The circuit of FIGURE Q28.4 has two resistors, with $R_{1} > R_{2}$ . Which of the two resistors dissipates the larger amount of power? Explain.

The circuit of FIGURE has two resistors, with $R_{1} > R_{2}$ . Which of the two resistors dissipates the larger amount of power? Explain.

Rank in order, from largest to smallest, the currents $I_{a}$ to $I_{d}$ through the four resistors in FIGURE

How much current flows through the bottom wire in $f i g u r e P 28.66$ , and in which direction ?

See all solutions

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