Question

What is the density ρh of hot air inside the balloon? assume that this density is uniform throughout the balloon. express the density in terms of th, tc, and ρc?

Answer 1

With the Ideal Gas formula.

Further Explanation

The ideal gas equation is an equation that presents the relationship between the pressure and volume of a gas with the temperature and the number of moles of the gas itself. This ideal gas equation is based on the laws of Boyle, Charles, and Avogadro.

This equation is generally written as

-PV = nRT

Boyle's Law (T = C)

Boyle's Law about the nature of gas was first created by Robert Boyle (1627¡1691). Boyle found experimentally that at a constant temperature, the pressure in a closed container would be inversely proportional to the volume of the gas. This means that if we press the gas and large volumes to small volumes, the gas pressure will rise, conversely if we expand the gas from small volumes to large volumes, the gas pressure will decrease. The process of pressing gas from large volumes to small volumes is called the compression process. While the process of changing the volume of gas from a small volume into a large volume is called the expansion process.

Gay Lussac Law (V = C)

The Gay Lussac Law was first coined by Joseph Louis Gay-Lussac (1778 - 1850) a chemist from France. Lussac's Gay Law states that under constant volume conditions, an increase in gas pressure will be directly proportional to an increase in gas temperature. This means that the gas in a closed container with a volume does not change (V0 = V1), so if the gas is heated from the initial temperature T0 to the final temperature T1 will cause the gas pressure also rises from the initial pressure (p0) to the final pressure (p1).

Charles Law (P = C)

Charles' ideal gas law is also called the law of constant pressure, first created by Jacques Alexandre Cesar Charles (1746 - 1823) a chemist from France. Charles's Law says "Under conditions of constant gas pressure, the volume of a gas will increase in proportion to the increase in temperature of the gas". This means that if we have a cylinder-piston system that can move up and down freely, then when the gas in the system is heated so that the temperature rises from T0 to T1, then to keep the gas pressure in the cylinder constant, the volume of gas will expand from the condition V0 to V1.

Learn more

 The ideal gas equation brainly.com/question/10599201

Details

Grade:  College

Subject:  Chemistry

keywords: Gas, the ideal gas.

Answer 2

Answer 1) : The density of the hot air inside the balloon can be found out by using ideal gas equation;

PV = nRT;

As n is number of moles and in gases, number of moles along with mass per mole is equal to the density of the gas.

If the moles in the gas are more the density will be more.

here, density (ρ) = mass (m) / volume (V); substituting in the ideal gas equation we get,

ρ = mP / RT

Answer 2) ρ (hot air) = ρ (cold air) X $\frac{T_{h}}{T_{c}}$

Here according to the formula because T(hot air) >T(cold air),

So, the density of hot air greater than the density of cold air.

The relationship between the ρ (h) = ρ(c) X $\frac{T_{h}}{T_{c}}$