An arctic weather balloon is filled with 23.2L of helium gas inside a prep shed. The temperature inside the shed is 5.°C. The balloon is then taken outside, where the temperature is 6.°C. Calculate the new volume of the balloon.You may assume the pressure on the balloon stays constant at exactly 1atm. Be sure your answer has the correct number of significant digits.L
Question
An arctic weather balloon is filled with 23.2L of helium gas inside a prep shed. The temperature inside the shed is 5.°C. The balloon is then taken outside, where the temperature is 6.°C. Calculate the new volume of the balloon.You may assume the pressure on the balloon stays constant at exactly 1atm. Be sure your answer has the correct number of significant digits.L
Solution
This problem can be solved using the ideal gas law, which states that the volume of a gas is directly proportional to its temperature, assuming pressure and the amount of gas are constant. This relationship is expressed in the formula V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
Step 1: Convert the temperatures from Celsius to Kelvin. The Kelvin scale is used in gas law problems because it is an absolute scale, starting at zero, which corresponds to absolute zero. The conversion formula is K = °C + 273.15.
T1 = 5°C + 273.15 = 278.15 K T2 = 6°C + 273.15 = 279.15 K
Step 2: Substitute the known values into the formula and solve for V2.
V1/T1 = V2/T2 23.2 L / 278.15 K = V2 / 279.15 K V2 = (23.2 L / 278.15 K) * 279.15 K V2 = 23.3 L
So, the new volume of the balloon when it is taken outside is 23.3 L.
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