A balloon of helium was put in the freezer at -23°C. Its volume at this temperature was 2.5 liters. It was removed from the freezer. Eventually, it reached a temperature of 177°C. What would its volume be at this temperature? (Neglect any force used to stretch the rubber balloon.)
Question
A balloon of helium was put in the freezer at -23°C. Its volume at this temperature was 2.5 liters. It was removed from the freezer. Eventually, it reached a temperature of 177°C. What would its volume be at this temperature? (Neglect any force used to stretch the rubber balloon.)
Solution
To solve this problem, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, provided the pressure and the amount of gas remain constant. The formula for Charles's Law is 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 all temperatures to Kelvin. The Kelvin scale is the standard unit of measure for temperature in physical sciences. 0°C is equal to 273.15K. So, -23°C is equal to 250.15K and 177°C is equal to 450.15K.
Step 2: Substitute the known values into the formula. So, we have 2.5L/250.15K = V2/450.15K.
Step 3: Solve for V2. Cross multiply to get V2 = (2.5L/250.15K) * 450.15K.
Step 4: Calculate the value to get V2 = 4.5 liters.
So, the volume of the helium balloon at 177°C would be 4.5 liters.
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