What happens to density of a gas as its volume decreases at constant pressure and temperature?

Question 5 Short/Long Answer Questions

Answer:

Solution:

As the temperature increases, volumes of most of the liquids also increases and when the volume increases density decreases. Similarly, when temperature decreases, the volume of most liquids decreases which increases the density. However, water shows anomalous behaviour. Water has maximum volume at 4-degree Celsius and maximum density at 4-degree Celsius.

But when water is cooled down further its volume starts increasing and hence, the density of water decreases when cooled further below than 4-degree celsius.

Hence, the density of water is maximum at 4-degree Celsius at $1\ g\ cm^{-3}$ or $1000\ kg\ m^{-3}$

Video transcript

"Hello students, welcome tornado learning question and answer video. We have an interesting question over here. How does the density of a liquid or gas vary with temperature? So is it increase the temperature what will happen with identity between the degrees of temperature what will happen to the density but before going there we should know what we mean by the degree, right? So let's say density of any substance is equal to Mars. I must tell you next one is defined with this first make note of this because this is very important. And this is what we will use to find out they are supposed to taste the liquid molecules. Now let's get some heat. So I let me make a burner here. This is my burner. Now, I start picking the molecules. So I am giving heat to the Wall Street or hand hitting the Olympics what happens when I give heat to the different the temperature will increase so when the temperature increases or when I make the temperature rise, so what happens is the liquid. Or so now what is the link we fight because the molecules will start behaving like this so they will start moving further and further and help expand or the volume will increase When the volume increases what will happen to the dentist the family of the victim or the supervisor for heresy handsome. So if the density is mass upon wondering its volume increases density is inversely proportional to the border, right? It wasn't increases in density will decrease so in case of liquid the density Decreases Increase in temperature, but we have an exception to this now. Let's talk about exception. Which liquid do you think is the exception yet? It is our very own water. So water behaves in an anomalous has a very peculiar what the hell's maximum volume. So let's say this is no experiment me that maximum. The water is at maximum volume is at 4 degrees Celsius and maximum density is at 4 degrees Celsius, but then when we cool the water or when we lower the temperature of water when we lower the temperature of water what will happen. So if temperature was increasing your volume was increasing himself. To be able to do this right but now when we lower the temperature cool the water further the volume starts increasing so in water, it happens the reverse that doesn't mean use the temperature volume start engraving and it keeps on increasing and the density of water increases and then decreases right? We saw that from here. So when the volume increases so density will decrease right? Right. So the water doesn't city of water decreases when pools further below 100 degrees celsius if you cool the water below 4 degrees Celsius, the density will decrease and in fact, that is the reason why I always a solid but it floats on water this property of water helps high school float on water to the density of Ice is actually less than that, of course. So this is just an exception. However, for most of the liquid this whole into orbit a that when we increase the temperature the density decreases and when we decrease the temperature the density increases, but will follow for most of the latest apart from what is this that is our exception. I hope this point was here. Thank you. "

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By Serm Murmson

The combined gas law is an equation that relates the pressure, temperature and volume of a gas. Based on this equation, you can predict what will happen to a sample of gas if you change one of the variables. If you decrease pressure and temperature simultaneously, you will not know the exact result unless you know the exact values by which each quantity decreased.

The combined gas law is a combination of Boyle's law and Charles's law. Boyle's Law states that the volume of a gas held at constant temperature is inversely proportional to its pressure. Charles's law states that the volume of a gas held at constant pressure is directly proportional to its temperature in Kelvins. The combined gas law is the combination of these two relationships into one equation.

The combined gas law states that the pressure of a gas is inversely related to the volume and directly related to the temperature. If temperature is held constant, the equation is reduced to Boyle's law. Therefore, if you decrease the pressure of a fixed amount of gas, its volume will increase. However, if you were to maintain a constant volume while decreasing pressure, the temperature would also have to decrease. The relationship of gases at a constant volume is given by Gay-Lussac's law. Gay-Lussac's law states that at constant volume, the pressure and temperature of a gas are directly proportional.

If you decrease the temperature of a fixed amount of gas at constant pressure, the combined gas law reduces to Charles's law. In this case, volume will also decrease. If you were to maintain a constant volume while decreasing the temperature, the pressure would also have to decrease in order to satisfy Gay-Lussac's law.

If you decrease both the pressure and temperature of a fixed amount of gas, any changes you observe will be in the volume of the gas. Temperature is directly related to volume, and pressure is inversely related to volume. Therefore, the resulting changes in volume will depend on the quantitative changes in both pressure and temperature. For example, if you decrease the temperature of the gas by a greater degree than the decrease in pressure, the volume will decrease. However, if you decrease the pressure by a greater degree than the decrease in temperature, the volume will increase.

Before doing any calculation, try to predict what you expect to happen to the density of a gas if pressure is increased while temperature is kept constant.

As you know, density is defined as the mass per unit of volume. Since the mass of the gas is also kept constant, the only way to change its density is to change the volume it occupies.

Now, what happens to the volume of an ideal gas when pressure is increased at constant temperature and number of moles?

You should remember from Boyle's Law that pressure and volume have an inverse relationship when temperature and number of moles of gas are kept constant.

What that tells you is that increasing the pressure of the gas will cause its volume to decrease. Likewise, decreasing the pressure of the gas will cause its volume to increase.

So right from the start you can say that since the pressure of the gas is increased, the volume will decrease, which in turn will cause the density of the gas to increase, since now you have the same mass of gas in a smaller volume.

If you start with #P_1# and #V_1# as the pressure and volume of the gas at an initial state, you can use Boyle's Law to write

#color(blue)(P_1 * V_1 = P_2 * V_2) -># the equation tha describes Boyle's Law

Here #P_2# and #V_2# are the pressure and volume of the gas at final state.

In your case, the pressure is doubled, so you can say that

#P_2 = 2 * P_1#

Plug this into the equation and solve for #V_2#

#V_2 = P_1/P_2 * V_1#

#color(purple)(V_2) = color(red)(cancel(color(black)(P_1)))/(2color(red)(cancel(color(black)(P_1)))) * V_1 = color(purple)( 1/2 * V_1)#

The density of the gas at the initial state was