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A balloon containing helium gas has a volume of 1.25 L at room temperature (23 oC). The balloon is heated to at temperature of 85 oC . Assuming no change in pressure, what is the new volume of the balloon?

User DanielKhan
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1 Answer

5 votes

Answer:


\boxed {\boxed {\sf 4.6 \ Liters}}

Step-by-step explanation:

The pressure stays constant, so we are dealing with volume and temperature, so we use Charles's Law. This states the temperature and volume of a gas are directly proportional. The formula is:


(V_1)/(T_1)=(V_2)/(T_2)

We know the original balloon has a volume of 1.25 liters at a temperature of 23 degrees celsius. These values can be substituted in.


(1.25 \ L)/(23 \textdegree C)=(V_2)/(T_2)

The new volume is unknown, but the temperature is increased to 85 degrees Celsius.


(1.25 \ L)/(23 \textdegree C)=(V_2)/(85 \textdegree C)

We are trying to solve for the new volume, V₂. It is being divided by 85 degrees Celsius. The inverse of division is multiplication, so we multiply both sides by 85°C.


85 \textdegree C*(1.25 \ L)/(23 \textdegree C)=(V_2)/(85 \textdegree C)*85 \textdegree C


85 \textdegree C*(1.25 \ L)/(23 \textdegree C)= V_2

The units of degrees Celsius cancel.


85 *(1.25 \ L)/(23) = V_2


4.61956522 \ L = V_2

The original measurements have at least 2 significant figures, so our answer must have 2. For the number we found, that is the tenth place.

  • 4.61956522

The 1 in the hundredth place (in bold above) tells us to leave the 6 in the tenth place.


4.6 \ L \approx V_2

The new volume of the balloon is approximately 4.6 liters.

User DRTauli
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