Thermodynamics - Find temperature of air in balloon

[thereddevils]

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 celsius 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

 

[thereddevils]

am i correct ?

 

[Rtjones]

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

 

[thereddevils]

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 !