10. A balloon has a volume of 0.5 L at 20°C. What will the volume be if the
balloon is heated to 150°C? Assume constant pressure and mass.
P1V1/T1=P2V2/T2, P1=P2
So, V1/T1=V2/T2
Solve for V2,
V1T2/T1=V2
Convert ºC to K using ºC+273.15K=K before plugging in the values and solving.
To find the final volume of the balloon when heated to 150°C, we can use Charles' Law, which states that the volume of a gas is directly proportional to its temperature, assuming constant pressure and mass.
Charles' Law equation:
V₁ / T₁ = V₂ / T₂
Where:
V₁ = Initial volume (0.5 L)
T₁ = Initial temperature (20°C)
V₂ = Final volume (unknown)
T₂ = Final temperature (150°C)
To solve for V₂, we rearrange the equation as follows:
V₂ = (V₁ × T₂) / T₁
Now, let's plug in the values:
V₂ = (0.5 L × 150°C) / 20°C
To simplify, convert the temperatures to Kelvin (K):
T₁ = 20°C + 273.15 = 293.15 K
T₂ = 150°C + 273.15 = 423.15 K
V₂ = (0.5 L × 423.15 K) / 293.15 K
V₂ ≈ 0.719 L
Therefore, when the balloon is heated to 150°C, its volume will be approximately 0.719 L.