A child receives a balloon filled with 27 L of
helium from a vendor at an amusement park.
The temperature outside is 304 K. What will
the volume of the balloon be when the child
brings it home to an air-conditioned house at
294 K? Assume that the pressure stays the
same.
Answer in units of L
(V1/T1) = (V2/T2)
6232
To solve this problem, we can make use of Charles's Law, which states that the volume of a gas is directly proportional to its temperature at constant pressure.
Step 1: Write down the given information:
Initial temperature (T1) = 304 K
Initial volume (V1) = 27 L
Final temperature (T2) = 294 K
Step 2: Apply Charles's Law equation:
V1 / T1 = V2 / T2
Step 3: Substitute the values:
27 L / 304 K = V2 / 294 K
Step 4: Cross-multiply and solve for V2:
(27 L) * (294 K) = (304 K) * V2
7926 L * K = 304 K * V2
Step 5: Simplify the equation:
7926 L * K = 304 K * V2
Step 6: Divide both sides by 304 K:
(7926 L * K) / (304 K) = (304 K * V2) / (304 K)
26.07 L = V2
Therefore, the volume of the balloon when the child brings it home to the air-conditioned house at 294 K will be 26.07 L.
To solve this problem, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
In this case, we are given that the pressure stays the same, so we can rewrite the equation as:
V1/T1 = V2/T2
Where:
V1 = Initial volume of the balloon (27 L)
T1 = Initial temperature (304 K)
V2 = Final volume of the balloon (what we need to find)
T2 = Final temperature (294 K)
Now we can solve for V2:
V2 = (V1 * T2) / T1
Substituting the given values:
V2 = (27 L * 294 K) / 304 K
Calculating this expression gives us:
V2 = 26.513 L
Therefore, the volume of the balloon when the child brings it home to an air-conditioned house at 294 K will be approximately 26.513 L.