Physics, 10.12.2019 20:31 ava5015

If you use such a tank to fill 0.020 m3 foil balloons (which don't stretch, and so have an internal pressure that is very close to atmospheric pressure), how many balloons can you expect to fill? assume the temperature is 20∘c.

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Answer from: livleluve76

The question is incomplete, here is a complete question.

Party stores sell small tanks containing 41 g of helium gas.

If you use such a tank to fill 0.020 m³ foil balloons (which don't stretch, and so have an internal pressure that is very close to atmospheric pressure), how many balloons can you expect to fill? Assume the temperature is 20°C.

Answer : The number of balloon filled can be, 12 balloons.

Explanation :

First we have to calculate the number of moles of gas in balloon.

Using ideal gas equation:

PV=nRT

where,

P = pressure of gas = 1 atm (atmospheric pressure)

V = volume of gas = 0.020m^3=20.0L (1m^3=1000L)

T = temperature of gas = 20^oC=273+20=293K

n = number of moles of gas = ?

R = gas constant = 0.0821 L.atm/mol.K

Now put all the given values in the ideal gas equation, we get:

$(1atm)\times (20.0L)=n\times (0.0821L.atm/mol.K)\times (293K)$

n=0.831mol

Thus, the number of moles of gas in balloon is 0.831 mol per balloon.

Now we have to calculate the mass of gas in balloon.

$\text{Mass of gas}=\text{Moles of gas}\times \text{Molar mass of gas}$

Molar mass of He gas = 4 g/mole

$\text{Mass of gas}=(0.831 mol/balloon)\times 4g/mol=3.32g/balloon$

Now we have to calculate the number of balloon can be filled.

Number of balloon filled = $\frac{41g}{3.32g/balloon}=12.3balloon\approx 12balloons$

Therefore, the number of balloon filled can be, 12 balloons.

Answer from: Quest

explanation:

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

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