Question

A hot air balloon has a volume of $2800{m^3}$ at $99^\circ C$ . What is the volume if the air cools to $80^\circ C$ ?

Answer 1

Hint: We have to know that, the gas laws were created toward the finish of the eighteenth century, when researchers started to understand that connections between pressing factor, volume and temperature of an example of gas could be acquired which would hold to guess for all gases.

Complete answer:
We have to know that Charles law, or the law of volume, was found in $1787$ by Jacques Charles. It expresses that, for a given mass of an optimal gas at steady pressing factor, the volume is straightforwardly corresponding to its supreme temperature, accepting in a shut framework. The assertion of Charles' law is as per the following, the volume ( $V$ ) of a given mass of a gas, at a consistent pressing factor ( $P$ ), is straightforwardly relative to its temperature ( $T$ ). As a numerical condition, Charles' law is composed as by the same token,
$V \propto T$
(or)
$\dfrac{V}{T} = {k_2}$
(or)
$\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}$
Where " $V$ " is the volume of a gas, " $T$ " is the outright temperature and ${k_2}$ is a proportionality constant (which isn't equivalent to the proportionality constants in different conditions in this article).
In the given details,
Initial volume $\left( {{V_1}} \right)$ = $2800$
Initial temperature $\left( {{T_1}} \right)$ = $99^\circ C = \left( {99 + 273} \right) = 372K$
Final temperature $\left( {{T_2}} \right)$ = $80^\circ C = \left( {80 + 273} \right) = 353K$
Final volume $\left( {{V_2}} \right)$ is calculated.
By using the above Charles law,
$\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}$
Rewrite the above expression to calculate the final volume.
${V_2} = \dfrac{{{V_1}{T_2}}}{{{T_1}}}$
Applying all the given values in the above expression,
${V_2} = \dfrac{{{V_1}{T_2}}}{{{T_1}}} = \dfrac{{2800 \times 353}}{{372}} = 2656.98{m^3}$
Therefore,
The final volume is $2656.98{m^3}$ .

Note:
We have to know that, other gas law Gay-Lussac's law, Amontons' law or the pressing factor law was found by Joseph Louis Gay-Lussac in $1808$ . It expresses that, for a given mass and consistent volume of an optimal gas, the pressing factor applied on the sides of its holder is straightforwardly corresponding to its supreme temperature.