A helium-filled balloon has a volume of 2.83 L
at 30
◦
C. The volume of the balloon decreases
to 2.35 L after it is placed outside on a cold
day. What is the outside temperature in K?
Answer in units of K?
(V1/T1) = (V2/T2)
T must be in kelvin.
To find the outside temperature in Kelvin (K), we need to use the base unit of temperature, which is Kelvin (K).
First, we convert the initial temperature from degrees Celsius (◦C) to Kelvin (K). To do that, we add 273.15 to the temperature in ◦C:
Initial temperature in K = Initial temperature in ◦C + 273.15
Given that the initial temperature is 30 ◦C, we can calculate:
Initial temperature in K = 30 + 273.15 = 303.15 K
Next, we need to find the final temperature in K. Since the balloon is placed outside on a cold day, we know that the final temperature is lower than the initial temperature. Since the balloon volume decreased, it means the gas inside the balloon is contracting due to colder temperatures.
To convert the final volume from liters (L) to cubic meters (m³), we need to divide it by 1000, since 1 L = 0.001 m³.
Final volume in m³ = Final volume in L / 1000
Given that the final volume is 2.35 L, we can calculate:
Final volume in m³ = 2.35 L / 1000 = 0.00235 m³
Assuming the pressure remains constant, we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
where P1 and P2 are the initial and final pressures (which are assumed to be constant in this case), V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.
We can rearrange the equation to solve for the final temperature:
T2 = (T1 * (P2 * V2)) / (P1 * V1)
Substituting the known values:
T2 = (303.15 K * (P2 * 0.00235 m³)) / (P1 * 2.83 L)
Since we don't have information about the pressures, we can assume they cancel out as they are constant. This leaves us with:
T2 ≈ (303.15 * 0.00235) / 2.83
Evaluating the equation:
T2 ≈ 0.7127
Therefore, the outside temperature in Kelvin (K) is approximately 0.7127 K.