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2 years ago

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A non-rigid balloon is held in a chamber set at 293 K and 1 atm of pressure. The balloon's volume is 0.05 m³. If the pressure in

the room is increased to 5
atm, what is the new volume of the balloon?

1 answer:

enyata [817]2 years ago

5 0

A non-rigid balloon is held in a chamber set at 293 K and 1 atm of pressure. The balloon's volume is 0.05 m³. If the pressure in the room is increased to 5 atm, then the new volume of the balloon would be 0.01 meter³

<h3>What is an ideal gas?</h3>

It is an imaginary gas for which the volume occupies by it is negligible, this gas does not exist in a practical situation and the concept of an ideal gas is only the theoretical one, the real gases approach the behaviors of an ideal gas at a very high temperature and very low pressure.

By using Boyle's law

P₁V₁=P₂V₂

Where P₁, and V₁, are initial pressure and volume

and P₂ and V₂, are the final pressure and volume

By substituting the values in the above equation

P₁ = 1 atm

V₁= 0.05 meter³

P₂ = 5.0 atm

V₂= ? meter³

The only unknown term which we have to find is the final volume of the balloon

1.0 ×0.05=5.0×V₂

V₂ =0.01 meter³

Thus, the new volume of the balloon would be 0.01 meter³

Learn more about ideal gas from here

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Explanation:

In the equation for the Decibel scale

$(1). \: \:\beta =10 log(\dfrac{I}{I_0})$

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And since

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Putting this into equation (1), we get:

$\boxed{ (2).\: \: \beta = 10log(\dfrac{r_0^2}{r^2})}$

Now, if the intensity is 100 dB when the distance is 5 meters, we have:

$100dB=10 log(\dfrac{r_02}{(5m)^2})$

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by taking both sides to the exponent:

$10^{10}= \dfrac{r_0^2}{25}$

$r^2 = 25 *10^{10}\\r = 5 *10^5$

Now equation (2) becomes

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when the intensity level is 85 dB we have

$85 = 10log(\dfrac{25*10^{10}}{r^2})$

$8.5 = log(\dfrac{25*10^{10}}{r^2})$

take both sides to exponents and we get:

$10^{8.5} =10^{ log(\dfrac{25*10^{10}}{r^2})}$

$10^{8.5} =\dfrac{25*10^{10}}{r^2}$

$r^2 = \dfrac{25*10^{10}}{10^{8.5}}$

$\boxed{r = 28.11m}$

Thus, $28.11m$ far from the speaker the intensity drops to 85 dB.

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