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?

Answer 1

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.