To determine the final volume of the balloon after heating it from 20°C to 25°C, we need to make certain assumptions and use the ideal gas law. The ideal gas law describes the relationship between the pressure (P), volume (V), and temperature (T) of a gas.
The ideal gas law is given by the equation: PV = nRT
Where: P = Pressure of the gas V = Volume of the gas n = Number of moles of the gas R = Ideal gas constant T = Temperature of the gas
To solve the problem, we need to assume that the pressure and the number of moles of gas remain constant throughout the process. With this assumption, we can rewrite the ideal gas law as:
(V1/T1) = (V2/T2)
Where: V1 = Initial volume of the balloon T1 = Initial temperature of the balloon V2 = Final volume of the balloon (what we want to find) T2 = Final temperature of the balloon
Now, let's plug in the given values into the equation:
(V1/293.15 K) = (V2/298.15 K)
Where 293.15 K is the initial temperature in Kelvin (20°C + 273.15 K) and 298.15 K is the final temperature in Kelvin (25°C + 273.15 K).
Rearranging the equation to solve for V2:
V2 = V1 * (T2/T1) = 4 liters * (298.15 K / 293.15 K)
Calculating the value:
V2 ≈ 4.03 liters
Therefore, the volume of the balloon after heating it to a temperature of 25°C will be approximately 4.03 liters.