Agas-filled weather balloon has a volume of 53.0 l at ground level, where the pressure is 751 mmhg and the temperature is 25.0 °c. after being released, the balloon rises to an altitude where the temperature is –2.01 °c and the pressure is 0.511 atm. what is the weather balloon's volume at the higher altitude?

Explanation:

In this problem we need to use the Ideal Gas Law, which is expressed like this:

Where is the pressure, is the volume, is the number of molecules, is the ideal gas constant and is the temperature.

Now, we need to apply the Ideal Gas Law to each case, at ground level and at the higher altitude.

Then, we will isolate , to use it later:

Now, we combined both equation, because is the same in both cases:

The problem asks about , so we isolate that volume and replace all known variables:

If we transform that volume into litres, we know that 1 litre is :

Therefore, the volume at the higher altitude is 8.14L

b.

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answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.