Question

15. A boy blows a balloon of volume 1 litre to pressure of 10 atmospheres
10 sec. the power is
1) 10.13 w 2) 101.3 w
3) 20.26 w
4) 0.506 w​

Answer 1

Answer:

Power = 10.13 w

Explanation:

Given

volume V = 1 L

pressure P = 10 atm ⇒ 101.33 J/ L

time t = 10 sec

Power = ??

Solution

As we know that

Power = w / t .....................(i)

and from pressure volume work

w = P dV .....................(2)

w = 101.33 X 1

w = 101.33 J

from equation (i)

Power = 101.33/ 10

Power = 10.13 w

Answer 2

The power is 10.13 W .

Given :

Initially balloon is not inflated , so $V_i=0\ L\ .$

Boy blows a balloon to 5 L , therefore , $V_f=1\ L = 10^{-3}\ m^3\ .$

Also , pressure , $P = 10\ atm = 1.013\times 10^5\ N/m^3$ .

Time taken , t = 10 sec .

We know , work done is given as product of increase in volume and pressure.

Therefore ,

$W=P\times \Delta V\\\\W=1.013 \times 10^5 \times ( V_f-V_i)\\\\W=1.013\times 10^5\times ( 10^{-3}-0)\\\\W=1.013\times 10^5 \times 10^{-3}\ J\\\\W=1.013\times 10^2\ J.$  

Now , Power P is given as :

$P=\dfrac{W}{t}\\\\P=\dfrac{1.013\times 10^2}{10}\\\\P=10.13\ W \ .$

Hence , this is the required solution .

Learn More :

Work , Power and Energy

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