Helium balloon problem adiabatic process

In summary, the conversation discussed the calculation of the volume and temperature of a large research balloon containing 2000 m^3 of helium gas at 1.00 atm and a temperature of 15.0 celsius as it rises rapidly to an altitude with an atmospheric pressure of 0.900 atm. The ideal gas law and adiabatic process equations were used to calculate the volume and temperature of the gas at the higher altitude. The resulting temperature was found to be 3.1 °C using the ideal gas law.
  • #1
kellya55
1
0

Homework Statement



A large research balloon containing 2000 m^3 of helium gas at 1.00 atm and a temperature of 15.0 celsius rises rapidly from ground level to an altitude at which the atmospheric pressure is only 0.900 atm (the figure (Figure 1) ). Assume the helium behaves like an ideal gas and the balloon's ascent is too rapid to permit much heat exchange with the surrounding air.Calculate the volume of the gas at the higher altitude?Calculate the temperature of the gas at the higher altitude?

Homework Equations

Adiabatic process

T1V1^gamma-1=T2V2^gamma-1 where gamma is 1.67 for helium

The Attempt at a Solution


Found volume of helium to be 2130 m ^3 which was correct but then kept on getting a temperature of around 3.-3.3 celsius(answer is to be given in celsius)using different vales for atm and gamma.It says that my rounding is off so I'll give step by step procedure of what I did
288.15 x 2000^0.67=T2 x 2130^0.67
and T2=276.24 and 276.24-273.15 is 3.1 celsius to 2 significant figures please help!
 
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  • #2
The temperature can be obtained easier (and with less error) using the ideal gas law:

PV/T=const.

The value for the new temperature is 3.1 °C.
ehild
 

Related to Helium balloon problem adiabatic process

1. What is the "Helium balloon problem" in regards to adiabatic processes?

The Helium balloon problem refers to the phenomenon where a helium balloon rises as it is heated due to an adiabatic process. This is because the gas inside the balloon expands as it is heated, causing the overall density of the balloon to decrease and allowing it to float.

2. Why is the adiabatic process important in understanding the behavior of helium balloons?

The adiabatic process is important because it helps explain why helium balloons rise when heated. It also plays a role in understanding the behavior of other gases in various situations, such as in weather patterns and industrial processes.

3. How does the temperature of the gas inside the helium balloon affect its behavior?

The temperature of the gas inside the helium balloon is directly related to its behavior. As the temperature increases, the gas expands and becomes less dense, causing the balloon to rise. Conversely, as the temperature decreases, the gas contracts and becomes more dense, causing the balloon to sink.

4. What is the difference between an adiabatic process and an isothermal process?

An adiabatic process is one where no heat is exchanged between the system and its surroundings, while an isothermal process is one where the temperature remains constant. In the case of a helium balloon, the expansion of the gas due to heating is an adiabatic process, while the balloon remaining at a constant height once it reaches equilibrium with the surrounding air is an isothermal process.

5. Can the "Helium balloon problem" be applied to other gases besides helium?

Yes, the Helium balloon problem can be applied to other gases, as long as they have a lower density than the surrounding air. This is because the principle behind the problem is based on the relationship between temperature, density, and buoyancy, which applies to all gases.

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