If a sample of gas is cooled at a constant pressure until it shrinks to one-fourth its initial volume, what change in its kelvin temperature must have occurred?

(V1/T1) =(V2/T2)

Since no initial volume is given I suggest you pick one that is convenient (make sure it divides by 3 evenly), then take 1/3 of that for V2.

To determine the change in the Kelvin temperature of the gas, we need to use Charles' Law. According to Charles' Law, at constant pressure, the volume of a gas is directly proportional to its Kelvin temperature.

The equation for Charles' Law is:

V₁ / T₁ = V₂ / T₂

Where:
V₁ = Initial volume of the gas
T₁ = Initial Kelvin temperature of the gas
V₂ = Final volume of the gas
T₂ = Final Kelvin temperature of the gas

From the problem statement, we know that the initial volume (V₁) of the gas is being shrunk to one-fourth (1/4) its initial volume (V₂ = 1/4 * V₁). We need to find the change in the Kelvin temperature (ΔT = T₂ - T₁).

Let's plug in the given values into the Charles' Law equation:

V₁ / T₁ = V₂ / T₂

V₂ = 1/4 * V₁

Therefore, substituting V₂ = 1/4 * V₁:

V₁ / T₁ = (1/4 * V₁) / T₂

Simplifying:

T₂ = T₁ * (V₁ / (1/4 * V₁))

T₂ = T₁ * (4 / 1)

T₂ = 4 * T₁

Therefore, the final Kelvin temperature is four times the initial Kelvin temperature.