A helium-filled balloon has a volume of 2.68 L at 15◦C. The volume of the balloon decreases to 2.33 L after it is placed outside on a cold day. What is the outside temperature in K? Answer in units of K.
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To answer this question, we need to apply Charles's Law, which states that the volume of a gas is directly proportional to its temperature, assuming pressure is constant.
To find the outside temperature in Kelvin (K), we can use the following formula:
V1/T1 = V2/T2
Where:
V1 = Initial volume of the balloon (2.68 L)
T1 = Initial temperature of the balloon (15°C + 273.15 K)
V2 = Final volume of the balloon (2.33 L)
T2 = Final temperature of the balloon (which we need to find)
Rearranging the formula to solve for T2, we get:
T2 = (V2 * T1) / V1
Now we substitute the known values:
T2 = (2.33 L * (15°C + 273.15 K)) / 2.68 L
Calculating this expression will give us the answer in Kelvin.
Convert 15°C to °K:
15°C = 15+273.15°K
= 288°K
Then use the ideal gas equation
PV=nRT
n=number of moles (constant in this case)
R=constant
Assume also that P=pressure constant, we have
V1/T1 = V2/T2
Solve for T2 to get
T2=V2*(T1/V1)
Substitute initial temperature T1, volume V1 and final V2 to find T2.