The temperature inside my refrigerator is about 40 Celsius. If I place a balloon in my fridge that initially has a temperature of 220 C and a volume of 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator?
Assuming you meant 40 degrees Celsius (not 40 Kelvin as that would be about -233 degrees Celsius), we need to convert the temperatures to Kelvin as that is the scale appropriate for thermodynamic calculations.
Initial temperature of the balloon = 220°C + 273.15 = 493.15 K
Final temperature of the balloon = 40°C + 273.15 = 313.15 K
We can use the combined gas law to solve for the final volume of the balloon:
(P1V1/T1) = (P2V2/T2)
We assume the pressure inside the balloon remains constant throughout the cooling process. This is a reasonable approximation as the pressure inside the balloon is much lower than the atmospheric pressure of the fridge, so any changes in pressure due to cooling will be negligible.
P1V1/T1 = P2V2/T2
Canceling out the pressure terms:
(V1/T1) = (V2/T2)
Solving for V2:
V2 = V1 (T2/T1)
Plugging in the values:
V2 = 0.5 L (313.15 K/493.15 K)
V2 = 0.318 L
Therefore, the volume of the balloon when it is fully cooled by the fridge is approximately 0.318 liters.
To find the final volume of the balloon when it is fully cooled by the refrigerator, we can apply the ideal gas law.
The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Since the pressure is constant within the refrigerator, we can simplify the ideal gas law equation to:
V1 / T1 = V2 / T2,
where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.
Let's convert the temperatures to Kelvin:
T1 = 220°C + 273.15 = 493.15 K
T2 = 40°C + 273.15 = 313.15 K
Now we can plug the values into the equation:
0.5 L / 493.15 K = V2 / 313.15 K
To solve for V2, we can cross-multiply and solve for V2:
V2 = (0.5 L * 313.15 K) / 493.15 K
V2 = 0.3175 L
Therefore, the volume of the balloon when it is fully cooled by the refrigerator will be approximately 0.3175 liters.