Coefficient of volume expansion of gas

In summary, the coefficient of volume expansion (γ) is calculated using the formula ∆V/V∆T and option 2 is the correct answer for its magnitude. The negative sign signifies that volume decreases with increasing temperature in this scenario and the coefficient is variable and inversely proportional to temperature.
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Homework Statement


coefficient.jpg


Homework Equations

The Attempt at a Solution



Coefficient of volume expansion γ = ∆V/V∆T

VT2 = constant

Differentiating we get ,

T2∆V + 2VT∆T = 0

∆V/V∆T = -2/T

So , option 2) looks right . Is that correct ?

How do I interpret the answer ? Does that mean the coefficient is a variable and is inversely proportional to temperature ? What does negative sign signify ?
 

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  • #2
Coefficient is negative as volume always decreases with increasing temperature in this scenario. Answer 2 is correct for the magnitude, and yes, it means the coefficient is variable and inversely proportional to temperature.
 
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  • #3
mjc123 said:
Coefficient is negative as volume always decreases with increasing temperature in this scenario. Answer 2 is correct for the magnitude, and yes, it means the coefficient is variable and inversely proportional to temperature.

Thanks !
 

What is the coefficient of volume expansion of gas?

The coefficient of volume expansion of gas is a measure of how much the volume of a gas changes with temperature. It is represented by the symbol α and is expressed in units of per degree Celsius (or Kelvin) −1.

What factors affect the coefficient of volume expansion of gas?

The coefficient of volume expansion of gas is affected by three main factors: the type of gas, the temperature, and the pressure. Each gas has its own unique coefficient of volume expansion, and higher temperatures and pressures generally result in a larger coefficient.

How is the coefficient of volume expansion of gas measured?

The coefficient of volume expansion of gas can be measured experimentally by observing the change in volume of a gas as it is heated or cooled. It can also be calculated using the ideal gas law, which relates the volume, pressure, and temperature of a gas.

How does the coefficient of volume expansion of gas affect everyday life?

The coefficient of volume expansion of gas plays a crucial role in many everyday processes, such as weather phenomena, heating and cooling systems, and the functioning of engines. It also helps in understanding the behavior of gases in different environments, such as in outer space.

What is the relationship between the coefficient of volume expansion of gas and the coefficient of thermal expansion?

The coefficient of volume expansion of gas and the coefficient of thermal expansion are closely related, as they both measure the change in size of a substance with temperature. However, the coefficient of volume expansion specifically applies to gases, while the coefficient of thermal expansion can apply to solids, liquids, and gases.

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