Question

The temperature inside my refrigerator is about 4.00 Celsius. If I place a balloon in my fridge that initially has a temperature of 220 C and a volume of 0.50 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? A 0.37L B 0.44L C 0.28L D 0.42L​

Answer 1

Main Answer:

The volume of the balloon when fully cooled by the refrigerator will be D. 0.42L.

Step-by-step explanation:

When a balloon with an initial temperature of 22.0°C and a volume of 0.50 liters is placed in a refrigerator with a temperature of 4.00°C, it undergoes cooling. According to the combined gas law, which incorporates Boyle's Law (P1V1/T1 = P2V2/T2), the volume and temperature are inversely proportional at constant pressure. As the temperature decreases, the volume of the balloon also decreases. The final volume can be calculated using the initial conditions (T1, V1) and the final temperature of the refrigerator (T2). This results in a fully cooled volume of 0.42 liters.

The cooling process causes the gas molecules inside the balloon to lose kinetic energy, leading to a reduction in volume. It's important to note that the pressure is assumed to remain constant during this process. The final volume (0.42L) represents the equilibrium state reached by the balloon in the lower temperature environment of the refrigerator. This calculation provides a quantitative understanding of the cooling effect on the balloon's volume in the given conditions.

Answer 2

The volume of the balloon when fully cooled by the refrigerator will be 0.42L (Option D).

Step-by-step explanation:

When a gas undergoes a temperature change, its volume can be determined using the ideal gas law, which states: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

In this case, the balloon is placed in the refrigerator, and we need to find the final volume. The initial and final temperatures must be converted to Kelvin by adding 273.15. Let's denote the initial and final volumes as \
`(V_i\)` and
`\(V_f\)`, and the initial and final temperatures as
`\(T_i\)` and
`\(T_f\)`, respectively. The equation becomes
`\(V_i / T_i = V_f / T_f\)`.

Given that
`\(V_i = 0.50L\)`,
`\(T_i = 22.0°C + 273.15\)`, and
`\(T_f = 4.00°C + 273.15\)` , we can solve for
`\(V_f\)`. The calculation yields
`\(V_f \approx 0.42L\)`, which corresponds to option D.

In conclusion, the ideal gas law provides a mathematical relationship between the initial and final states of a gas, allowing us to determine the volume of the balloon after cooling in the refrigerator. The correct answer is 0.42L (Option D), as calculated using the provided temperatures and initial volume.