Answer:
497 K
Explanation:
Assuming that the volume of the balloon (and so, the gas) remains constant, we can solve the problem by using the pressure's Law:
"When a constant mass of an ideal gas is kept at constant volume, the pressure of the gas is directly proportional to its absolute temperature"
Mathematically:
[tex]p\propto T[/tex]
where
p is the pressure of the gas
T is the absolute temperature
The equation can also be rewritten as
[tex]\frac{p_1}{T_1}=\frac{p_2}{T_2}[/tex]
where:
[tex]p_1 = 3 atm[/tex] is the initial pressure of the gas
[tex]T_1=298 K[/tex] is the initial temperature of the gas
[tex]p_2 = 5 atm[/tex] is the final pressure of the gas
Solving for T2, we find the final temperature:
[tex]T_2=\frac{p_2 T_1}{p_1}=\frac{(5)(298)}{3}=497 K[/tex]
