To find the new volume of the balloon when placed in a hot room, we can use Charles's Law, which relates the volume and temperature of a gas at constant pressure. The law is given by:
[tex]\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\][/tex]
where:
- [tex]\( V_1 \)[/tex] is the initial volume of the gas,
- [tex]\( T_1 \)[/tex] is the initial temperature of the gas (in Kelvin),
- [tex]\( V_2 \)[/tex] is the final volume of the gas,
- [tex]\( T_2 \)[/tex] is the final temperature of the gas (in Kelvin).
First, let's convert the given temperatures from Celsius to Kelvin:
[tex]\[
T_1 = 25.0^{\circ}C + 273.15 = 298.15\, K
\][/tex]
[tex]\[
T_2 = 40.0^{\circ}C + 273.15 = 313.15\, K
\][/tex]
Next, we rearrange the formula to solve for the final volume [tex]\( V_2 \)[/tex]:
[tex]\[
V_2 = V_1 \times \frac{T_2}{T_1}
\][/tex]
Substitute the known values into the equation:
[tex]\[
V_2 = 3.50\, L \times \frac{313.15\, K}{298.15\, K}
\][/tex]
Now, we calculate:
[tex]\[
V_2 \approx 3.50 \times 1.050351
\][/tex]
[tex]\[
V_2 \approx 3.676
\][/tex]
Hence, the new volume of the balloon in the hot room is approximately [tex]\( 3.68 \, L \)[/tex].
From the given options:
- 2.19 L
- 3.33 L
- 3.68 L
- 5.60 L
The correct answer is:
[tex]\[
\boxed{3.68}
\][/tex]
