How Does Temperature Change with Volume in a Quasi-Static Adiabatic Process?

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In a quasi-static adiabatic process for an ideal gas, the relationship TV^(γ-1) = constant holds true, indicating that temperature and volume are inversely related under adiabatic conditions. To find the radius at which the temperature drops to 2000 K after a uranium fission bomb detonation, the Ideal Gas Law and the adiabatic process equation PV^γ = constant can be applied. The initial conditions involve a gas sphere with a radius of 50 ft and a temperature of 300,000 K. Calculating the new radius requires understanding the changes in volume and temperature as the gas expands. This analysis is crucial for understanding the thermodynamic behavior of gases in explosive scenarios.
shaiqbashir
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Hello Friends!

can anybody help me?

show that for a quasi static adiabatic process of an ideal gas, the following reaction holds

TV^{\gamma-1}}=constant

Secondly:::

At about 100ms after detonation of a uranium fission bomb, the "ball of fire" cosists of a sphere of gas with a radius of about 50 ft and a temperature of 300,000 degree Kelvin. At what radius is the temperature 2000 K?
 
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For the First:

Use Ideal Gas Law and the Equation for adiabatic process PV^{\gamma}=constant
 

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