A fixed mass of gas of volume 600 cm cube at a temperature of 27 C is cooled at constant pressure to a temperature of 0C.what is the change in volume
P V = nRT
n constant
P constant
so
P2 V2 / T2 = P1 V1 / T1
V2 = (P1/P2)(T2/T1) V1
but P is constant
V2 = (T2/T1)V1
T2 = 273
T1 = 300
so V1 less than 600
V2-V1 , the change, is negative
To find the change in volume, we can use Charles's Law, which states that the volume of a given amount of gas is directly proportional to its temperature when pressure is held constant. Charles's Law can be mathematically expressed as V1/T1 = V2/T2.
In this case, we have the initial volume (V1 = 600 cm³), the initial temperature (T1 = 27 °C = 27 + 273 = 300 K), and the final temperature (T2 = 0 °C = 0 + 273 = 273 K). We need to find the final volume (V2).
Using Charles's Law, we can rearrange the equation to solve for V2:
V1/T1 = V2/T2
600 cm³ / 300 K = V2 / 273 K
Cross-multiplying and simplifying the equation, we get:
V2 = (600 cm³ * 273 K) / 300 K
V2 = 546 cm³
Therefore, the change in volume is 546 cm³.