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The initial temperature of a balloon is 25 degrees Celsius. This is K.

How hot will a 2.3 L balloon have to get to expand to a volume of 4.6 L? K , or
Celsius..

The initial temperature of a balloon is 25 degrees Celsius. This is K. How hot will-example-1

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The temperature that the balloon must reach to expand to a volume of 4.6 L is 596 Kelvin.

To solve this problem, we can use Charles' Law, which states that the volume of a gas is directly proportional to its temperature, as long as a constant pressure is maintained.

The mathematical formula for Charles' Law is:


\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(V_1)/(T_1)=(V_2)/(T_2) } \end{gathered}$} }

Where:

  • V₁ is the initial volume
  • T₁ is the initial temperature
  • V₂ is the final volume
  • T₂ is the final temperature

In this case, we have the following values:

  • V₁ = 2.3 L
  • T₁ = 25 °C + 273 = 298 K
  • V₂ = 4.6 L
  • T₂ = ?

We can rearrange the Charles Law formula to solve for T₂:


\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=(V_2T_1)/(V_1) } \end{gathered}$} }

Where:

  • V₁ is the initial volume
  • T₁ is the initial temperature
  • V₂ is the final volume
  • T₂ is the final temperature

Substituting the known values:


\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=\frac{(4.6 \\ot{L}*298 \ K) }{2.3\\ot{L}} } \end{gathered}$} }


\boxed{\bf{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=596 \ Kelvin=323 \ ^(\circ)C } \end{gathered}$} }}}

The temperature that the balloon must reach to expand to a volume of 4.6 L is 596 Kelvin.

NOTE: The temperature in degrees Celsius (°C), in these types of exercises are always converted into Kelvin (K).

User Mike Dalrymple
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