Answer: cp is more than CV because when a gas is heated at constant volume, the entire amount of heat given is utilised to raise the temperature. When a gas is heated at **constant pressure**, however, the heat given is used to raise both the temperature and volume of the gas. Therefore, in order for constant-pressure heating to use all the available heat, the heater must be able to deliver much more power than when heating at constant volume.

What is the significance of CP being bigger than CV? When a gas is heated at a **constant volume**, the work done on the gas raises the system's internal energy. Cp is larger than Cv, the molar specific heat at constant volume, since energy must now be given not only to raise the temperature of the gas but also to allow the gas to do work. If we assume that the gas can be treated as an ideal gas and use the formula CV=nRT, where n is the number of moles of gas, then we can say that more work needs to be done to increase the pressure of a gas by **a certain amount** if we assume that the gas is monatomic.

Here is how CP compares to CV for a monatomic gas:

CP = k*T^3 = n*cv*T^3 = n*(4/3)*pi^2*k*T^3 = 4/3*pi^2*n*k*T^3 = 2/3*pi^2*n*h*T^3

So, CP is bigger than CV because it takes **more work** to increase the pressure of the gas by a certain amount when compared to **its rise** in temperature. This is why CP is always bigger than CV when a gas is heated at a constant volume.

It is obvious that the two heat capacities are not equivalent, with CP being bigger than CV by a factor linked to labor done. 2. Because the system does no work at **constant volume**, the entire heat absorbed is used to raise the temperature of the system. As a result, CP is bigger than CV. 1.

Cp is nearly equivalent to cv for solids and most liquids. When we limit the volume of the gas and do not allow it to expand, it takes **less heat** to raise **its temperature** by 1K, thus vc/cv is very close to (but not exactly) the thermal conductivity of the fluid.

For example, if we fill a glass tube with water and suspend it over a flame, the water will quickly boil because the heat from the fire can easily reach all the way down into the glass tube. If we limit the amount of water that can evaporate by using **a vacuum pump**, then more water can be brought to a boil than if there were no restriction on the flow of water out of the glass tube.

So, boiling point elevation is significant in chemistry because it tells us about the nature of certain substances. For example, the boiling point of sodium is about 990°C (19,000°F), while the boiling point of chlorine is about 19°C (36°F). So, boiling point elevation is a useful tool for separating these elements from each other. It also helps us identify other elements based on their effects on water: alkalis have a strong effect, acids have a weak effect, and metals have no effect at all on the boiling point of water.

When the system is at **constant pressure**, Cp is the amount of heat necessary to increase the temperature of **a unit mass** (1 kg) by **one degree Celsius**. And CV is the amount of heat necessary to increase the temperature of a unit mass by one degree Celsius while the system volume is constant. Then Cp = CV. This equation shows that the larger the surface area, the more heat must be added to cause a change in temperature.

As far as I know, Cp is the amount of energy required to increase the temperature of 1 kg of water by 1 degree Celsius. That's it! The rest is just math. Heat capacity depends on the size of the molecule, so smaller molecules require more energy than larger ones to reach the same temperature. But since we are talking about the universe here, there is no such thing as a small particle or large molecule. So don't worry about this detail. All you need to know is that hydrogen has a very low heat capacity because it is so easy to burn, and oxygen has a high heat capacity because it doesn't melt even when heated very intensely. Thus, compounds with elements from both groups will have an average heat capacity.

Cp is also called thermal capacitance because it is the amount of heat needed to increase the temperature of a substance by one degree Celsius when some other factor is not changing (the system volume is constant).

Answer

- Expression for Cp. Cp is the amount of heat capacity required to raise the temperature of substance by one degree at constant pressure. So we have.
- Expression for Cv. Cv is the amount of heat required o raise temperature of body by one degree at constant volume.
- Cp is greater than Cv. Cp = (5/2) R and Cv= (3/2) R.

CP's value is always bigger than CV's value. At absolute zero temperatures, however, CP = CV. Thus, at absolute temperature, CP=CV for **actual gases**.

The ratio of CP to CV is called the compressibility factor. It is a number between 0 and 1 that indicates how much more difficult it is for a gas to be compressed as its temperature increases.

For example, if we say that CP for hydrogen is 2 and CV is 1, this means that it takes twice as much pressure to make 1 molar volume of hydrogen as it does oxygen. This can be understood by looking at **the boiling points** of these gases: hydrogen has a boiling point of **20 degrees Celsius** while oxygen has a boiling point of -80 degrees Celsius. So, even though hydrogen is less dense than oxygen, it becomes easier to compress as you increase the temperature.

As **another example**, let's say that CP for nitrogen is 7 and CV is 4. This would mean that it takes seven times as much pressure to make one molar volume of nitrogen as it does oxygen. The boiling point for nitrogen is 77 degrees Celsius which is much higher than that of oxygen. So, even though nitrogen is less dense than oxygen, it becomes easier to compress as you increase the temperature.

In a nutshell, the particular temps The specific temperatures of the component gases do not produce the Cp and CV of a gas combination. They are equivalent to the sum of (mass fraction x heat specific) for a single gas. Multiply by **the mass fractions** if cp or cv is provided in kJ/kgK. If the data are given for volumes, then multiply by 1.38066 (volume fraction). For example, calcuate the Cp of CO compared with H2 using the following steps: First, convert the concentrations into masses using **the molar masses**. Then, add the component heat capacities. Finally, divide by 1029 J/kmol.

There are many websites that will calculate the Cp of compounds for you. Here are two examples: http://www.thermodynamicslibrary.com/cpmix.html and https://webhome.phy.duke.edu/~rtyler/classes/chem101/Mixing_Concentrations.html

The main advantage of **this method** is that it requires **only three values**: one temperature and two concentrations. The disadvantages are that this method assumes constant volume and constant pressure conditions. It also requires knowledge of the molecular weights of the components.

As you can see, there are many different methods available for calculating the Cp of mixtures. It depends on your situation.