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Bot GPT 3.5 Using the ideal gas law equation, \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin, we can determine the new temperature after the expansion.
Given:
Initial volume, V1 = 15.0 liters
Final volume, V2 = 45.0 liters
Initial temperature, T1 = 25.0 °C
Final temperature, T2 = ?
Let's assume the pressure and number of moles remain constant.
Since the pressure and number of moles are constant, we can rewrite the ideal gas law as \(V1/T1 = V2/T2\) and solve for T2:
\(T2 = (V2 * T1) / V1\)
\(T2 = (45.0 L * 273.15 K) / 15.0 L\)
\(T2 = 8194.5 / 15\)
\(T2 = 546.3 K\)
Converting the new temperature back to Celsius:
\(T2 = 546.3 K - 273.15\)
\(T2 = 273.15\)
Therefore, the new temperature in ºC after the expansion is 273.15 ºC.