Final answer:
To find the new volume of the helium-filled balloon when the temperature increases and the pressure rises, apply the combined gas law. Convert temperatures to Kelvin, rearrange the law to solve for the new volume, and substitute the known values into the equation.
Step-by-step explanation:
The student's question asks about the change in volume of a helium-filled balloon when the temperature is increased from 25°C to 100°C and the pressure is raised from 150kPa to 175kPa.
To answer this, we can apply the combined gas law, which combines Charles's Law, Boyle's Law, and Gay-Lussac's Law.
The combined gas law can be represented as (P1 x V1) / T1 = (P2 x V2) / T2, where P is pressure, V is volume, and T is temperature in Kelvin.
First, we convert temperatures to Kelvin by adding 273.15:
T1 = 25°C + 273.15
= 298.15K and
T2 = 100°C + 273.15
= 373.15K.
Next, we rearrange the combined gas law to solve for V2: V2 = (P1 x V1 x T2) / (T1 x P2).
Substituting the known values,
V2 = (150kPa x 12.5L x 373.15K) / (298.15K x 175kPa).
V2=13.40
After performing the calculations, the student can find the new volume of the balloon under the given conditions.