Thermodynamics - Find temperature of air in balloon

In summary, when a hot-air balloon is heated, some air escapes and the pressure inside the balloon remains constant at just above atmospheric pressure. The mass and volume of air in the balloon just before it rises are 300 kg and 400 m^3 respectively.
  • #1
thereddevils
438
0

Homework Statement


The air inside a hot-air balloon is heated up from a density of 1.25 km/m^3 and a temperature of 27 degree celcius until the balloon begins to float . During the heating process , some air escapes from the balloon and the pressure inside the balloon remains constant at just above the atmosphric pressure . THe mass and volume of air in the balloon just before it rises are 300 kg and 400 m^3 respectively . The temperature of hot ait is ??


Homework Equations



Charles law and Boyle's law

The Attempt at a Solution



From Charles law , v1/T1=v2/T2

v1/27=400/T2

so i need to find V1 first before i can get T2 , i attempt to make use the other info given .

density = m/v

is the mass of the gas still the same after the expansion ? i don think so > i am not sure how to get v1
 
Physics news on Phys.org
  • #2


am i correct ?
 
  • #3


Hey,

I just typed up this awesome response and then the web browser crapped out on me... so I'm going to summarize. I hope this is still just as helpful

Okay so the assumption within the problem is that the pressure remains constant. KEEP THAT IN MIND.

Now use this equation for density... density = MP/(RT) where R is the universal gas constant, P is the pressure, M is the molar mass, and T is the absolute temperature.

Okay cool so let's rearrange the equation to have density*T = MP/(R).

From here we know that since pressure is constant, MP/(R) will be constant throughout the equation. So just set the initial and final density and temp equal to each other and wham bam money gram. Density(i)*T(i) = Density(f)*T(f).

I think this is right... Cheers
 
  • #4


Rtjones said:
Hey,

I just typed up this awesome response and then the web browser crapped out on me... so I'm going to summarize. I hope this is still just as helpful

Okay so the assumption within the problem is that the pressure remains constant. KEEP THAT IN MIND.

Now use this equation for density... density = MP/(RT) where R is the universal gas constant, P is the pressure, M is the molar mass, and T is the absolute temperature.

Okay cool so let's rearrange the equation to have density*T = MP/(R).

From here we know that since pressure is constant, MP/(R) will be constant throughout the equation. So just set the initial and final density and temp equal to each other and wham bam money gram. Density(i)*T(i) = Density(f)*T(f).

I think this is right... Cheers

thank you Jones , its indeed an awesome response !
 

1. What is the formula for finding the temperature of air in a balloon?

The formula for finding the temperature of air in a balloon is: T = (P * V)/(n * R), where T is the temperature in Kelvin, P is the pressure in atmospheres, V is the volume in liters, n is the number of moles of gas, and R is the ideal gas constant (0.0821 L*atm/mol*K).

2. How does the temperature affect the volume of air in a balloon?

The temperature of the air in a balloon directly affects its volume. According to Charles' Law, as the temperature increases, the volume of the gas also increases. This is because the molecules in the gas have more kinetic energy and move further apart, increasing the volume.

3. Can the temperature of air in a balloon change without changing its pressure or volume?

No, according to the Ideal Gas Law, the temperature of a gas is directly proportional to its pressure and volume. Therefore, if the pressure and volume remain constant, the temperature cannot change.

4. Is it possible for the air in a balloon to have a negative temperature?

No, it is not possible for the air in a balloon to have a negative temperature. According to the Kelvin scale, which is based on absolute zero, the lowest possible temperature is 0 Kelvin (-273.15 degrees Celsius). Negative temperatures do not exist in this scale.

5. How does the type of gas in a balloon affect its temperature?

The type of gas in a balloon does not affect its temperature, as long as the pressure, volume, and number of moles remain constant. The Ideal Gas Law applies to all gases, regardless of their chemical properties.

Similar threads

  • Introductory Physics Homework Help
Replies
12
Views
475
  • Introductory Physics Homework Help
Replies
8
Views
633
  • Introductory Physics Homework Help
5
Replies
170
Views
4K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
6K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
7K
  • Introductory Physics Homework Help
Replies
11
Views
3K
  • Introductory Physics Homework Help
Replies
16
Views
1K
Back
Top