How Does Temperature Affect Water Overflow and Gas Behavior in Physics Problems?

[Kickbladesama]

need help on three problems fast!

Homework Statement

A cylindrical brass container with a base of 87.0 cm2 and height of 20.0 cm is filled to the brim with water when the system is at 25.0°C. How much water overflows when the temperature of the water and the container is raised to 94.5°C? (The coefficient of volume expansion for water and brass are 207 multiplied by 10-6 K-1 and 57 multiplied by 10-6 K-1, respectively.)

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At 0.0°C and 1.00 atm, 0.95 mol of a gas occupies a volume of 0.0213 m3.
(a) What is the number density?
(b) Estimate the average distance between the gas molecules.
(c) If the gas is composed of diatomic molecules with a molecular mass of 29.16500 g/mol, what is the total mass?
(d)What is the mass density?

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A sealed cylinder contains a sample of ideal gas at a pressure of 1.1 atm. The rms speed of the molecules is v0. If the rms speed is then reduced to 0.73v0, what is the pressure of the gas?

Homework Equations

pV = NRT

deltaL/L = alpha x temp

The Attempt at a Solution

 

[tiny-tim]

Hi Kickbladesama!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

 

[thomate1]

For the first problem, we can use the formula for volume expansion to find the new volume of the water and container at 94.5°C:

V2 = V1(1+αΔT)

Where V1 is the original volume, α is the coefficient of volume expansion, and ΔT is the change in temperature.

We can then use the formula for density to find the amount of water that overflows:

ρ = m/V

Where ρ is the density, m is the mass of the water, and V is the volume.

For the second problem, we can use the ideal gas law to find the number density and the mass density:

N/V = p/RT

Where N is the number of molecules, V is the volume, p is the pressure, R is the gas constant, and T is the temperature.

To find the average distance between molecules, we can use the formula:

d = (√(3V/N))^(1/3)

Where d is the average distance, V is the volume, and N is the number of molecules.

For the third problem, we can use the formula for the rms speed of gas molecules:

v = √(3RT/M)

Where v is the rms speed, R is the gas constant, T is the temperature, and M is the molecular mass.

We can then use the ideal gas law to find the new pressure:

p2 = p1(v2/v1)^2

Where p1 is the original pressure, v1 is the original rms speed, and v2 is the new rms speed.

I hope this helps with your homework. Remember to always show your work and use the appropriate units in your calculations. Good luck!