Answer: 1.47
Explanation:
The combined gas equation when pressure is constant:
[tex]\frac{V_1}{n_1T_1}=\frac{V_2}{n_2T_2}[/tex]
where,
[tex]n_1[/tex] =original number of moles of air in the balloon = ?
[tex]n_2[/tex] = number of moles of air in the heated balloon = ?
[tex]V_1[/tex] = initial volume of gas = [tex]3000m^3[/tex]
[tex]V_2[/tex] = final volume of gas = [tex]5000m^3[/tex]
[tex]T_1[/tex] = initial temperature of gas = [tex]21^oC=273+21=294K[/tex]
[tex]T_2[/tex] = final temperature of gas = [tex]60^oC=273+60=333K[/tex]
Now put all the given values in the above equation, we get the final pressure of gas.
[tex]\frac{3000}{n_1\times 294K}=\frac{5000}{n_2\times 333K}[/tex]
[tex]\frac{n_2}{n_1}=1.47[/tex]
Therefore, the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon is 1.47
