Assume that you have a cylinder with a movable piston. What...

Assume that you have a cylinder with a movable piston. What would happen to the gas volume of the cylinder if you were to do the following? (a) Halve the Kelvin temperature while holding the pressure constant (b) Increase the amount of gas by 1$/ 4$ while holding the temperature and pressure constant (c) Decrease the pressure by 75$\%$ at constant $T$ (d) Double the Kelvin temperature, and double the pressure

Assume that you have a cylinder with a movable piston. What would happen to the gas volume of the cylinder if you were to do the following?
(a) Halve the Kelvin temperature while holding the pressure constant
(b) Increase the amount of gas by 1$/ 4$ while holding the temperature and pressure constant
(c) Decrease the pressure by 75$\%$ at constant $T$
(d) Double the Kelvin temperature, and double the pressure

Key Concepts

Boyle's Law

Boyle's Law states that the volume of a gas is inversely proportional to its pressure when the temperature and the number of particles remain constant. This principle helps in understanding how a reduction in pressure results in an increase in volume, and vice versa, under isothermal (constant temperature) conditions.

Avogadro's Law

Avogadro's Law establishes that the volume of a gas is directly proportional to the number of moles of gas when the temperature and pressure are constant. This concept explains how adding more gas particles increases the volume of the gas and is essential when considering changes in the amount or moles of the gas.

Ideal Gas Law

The ideal gas law (PV = nRT) connects pressure (P), volume (V), the number of moles (n), and Kelvin temperature (T) through the gas constant (R). This law provides a framework to understand how changes in one variable affect the others under ideal conditions. It is fundamental for analyzing scenarios involving gas expansion or compression when multiple parameters are modified simultaneously.

Charles' Law

Charles' Law states that the volume of a gas is directly proportional to its Kelvin temperature when the pressure and amount of gas are held constant. This concept is crucial for understanding how a decrease in temperature leads to a reduction in volume and an increase in temperature leads to an expansion of the gas.

Transcript

00:01 This problem gives us a sample of gas shown right here, and it's asking us to find, to show the new sample of gas when we decrease the temperature by one -half, when we increase the number of moles by one -fourth, when we decrease the pressure by 3 -4s, or 75%, and then when we double the temperature, and we also double the pressure.

00:24 So to do this, we need to use the ideal gas law.

00:27 So the ideal gas law is pv equals n r t.

00:31 And we need to find the equation of proportionality for volume, because we need to show the sample of gas, so we need to know how the volume is changing.

00:40 So volume is proportional to n times t over p.

00:47 And i just didn't include r because r is a constant, and so that means it's going to stay the same.

00:53 So for the first one, we're decreasing temperature by one half.

00:57 So volume is proportional to one half.

01:03 And in this case, the number of moles and pressure is staying constant.

01:07 So the only thing that's changing is that this volume is going to be one half of the original volume.

01:13 So we can just draw that if we do a dotted line at this level.

01:23 So then for the next one, we'll do the same thing.

01:25 So volume is proportional to.

01:28 So n is in the numerator, just like temperature was.

01:31 So this one's going to increase by one fourth.

01:35 So we can write, we can do either five -fourths or we can do, it's easier for me to think about it as 1 .25...