# Question #46e82

##### 1 Answer

Here's what I got.

#### Explanation:

As it is written, your problem doesn't provide enough information to allow for a solution to be formulated *exclusively* in terms of the original volume of the balloon.

More specifically, you would need to know the density of seawater at that depth and temperature.

With this being said, I will assume that the density of seawater at that depth is about

Now, the idea here is that the *number of moles* of gas and its *temperature* will **remain constant** as the balloon makes its way to **decreases** with depth,

Even if that were not the case, the insufficient data would force you to assume temperature constant anyway.

Now, *pressure* and *volume* have an **inverse relationship** when number of moles and temperature are kept constant - this is known as Boyle's Law.

Mathematically, this is written like this

#color(blue)(P_1V_1 = P_2V_2)" "# , where

At the surface of the Earth, atmospheric pressure is equal to

The pressure exerted by *a fluid* at a depth

#color(blue)(P_h = rho * g * h)" "# , where

Before plugging in your values, convert the density from *grams per milliliter* to *kilograms per cubic meter*

#1.025 color(red)(cancel(color(black)("g")))/(color(red)(cancel(color(black)("mL")))) * "1 kg"/(1000color(red)(cancel(color(black)("g")))) * (10^6color(red)(cancel(color(black)("mL"))))/"1 m"^3 = "1025 kg/m"^3#

The pressure exerted by the *seawater* at

#P_"water" = 1025 "kg"/"m"^3 * 9.81"m"/"s"^2 * "130 m"#

#P_"water" = "1,307,182.5" overbrace("kg"/("m s"^(2)))^(color(blue) (="Pa"))#

#P_"water" = "1,307,182.5 Pa"#

The **total pressure** exerted on the balloon will include the atmospheric pressure

#P_"total" = P_"atm" + P_"water"#

#P_"total" = "101,325 Pa" + "1,307,182.5 Pa" = "1,408,507.5 Pa"#

Rearrange the Boyle Law equation and solve for

#P_1V_1 = P_2V_2 implies V_2 = P_1/P_2 * V_2#

Here

#V_2 = ("101,325" color(red)(cancel(color(black)("Pa"))))/("1,408,507.5" color(red)(cancel(color(black)("Pa")))) * V_1#

#V_2 = 0.07194 * V_1#

Rounded to two sig figs, the answer will be

#V_2 = color(green)(0.072 * V_1)#