A diatomic ideal gas quesion

In summary, in a diatomic ideal gas expanding at constant pressure, 100% of the heat supplied is used to increase the internal energy and 0% is used to do expansion work. The equations Q=CnT and C_p=\frac{7}{2}R are used to determine this.
  • #1
wowolala
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Homework Statement



A diatomic ideal gas expands at constant pressure. What percentage of the heat supplied to the gas is used to increase the internal energy of the gas? what percentage is used to do expansion work?

i know Q=CnT, and in the diatomic ideal gas, C_p= [tex]\frac{7}{2}[/tex] R. but i am so confused that the number of moles, n is not given, and T is also is not given, how get we start with this question...

thx. can someone help me
 
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  • #2
explain this?Homework Equations Q=CnTC_p= \frac{7}{2} RThe Attempt at a SolutionSince the gas is expanding at constant pressure, its temperature will remain constant. This means that the heat supplied to the gas (Q) will be equal to the increase in the internal energy of the gas (C_p n T). Since the temperature is constant, all of the heat supplied will be used to increase the internal energy. Therefore, 100% of the heat supplied is used to increase the internal energy and 0% is used to do expansion work.
 
  • #3


I would suggest starting with the basics of thermodynamics to solve this problem. The first law of thermodynamics states that the change in internal energy of a system is equal to the heat supplied to the system minus the work done by the system. In this case, since the gas is expanding at constant pressure, the work done by the gas is equal to the pressure times the change in volume.

Next, we can use the ideal gas law, PV = nRT, to relate the pressure, volume, and number of moles of the gas. Since the gas is diatomic, we know that n = 2 for every molecule of gas. However, since the number of moles is not given, we can simply use a general value, such as n = 1, for our calculations.

Now, we can substitute these values into the first law of thermodynamics equation to get:

ΔU = Q - W = Q - PΔV

We also know that the heat supplied to the gas is equal to the change in internal energy plus the work done by the gas, so we can write:

Q = ΔU + W = ΔU + PΔV

Substituting this into our original equation, we get:

ΔU = (ΔU + PΔV) - PΔV

Now, we can solve for the percentage of heat used to increase internal energy and the percentage used to do expansion work:

Percentage of heat used to increase internal energy = (ΔU / Q) * 100%

Percentage of heat used to do expansion work = (PΔV / Q) * 100%

Since we do not have specific values for the change in internal energy, pressure, and volume, we cannot calculate the exact percentages. However, we can see that the percentage of heat used for internal energy will be higher than the percentage used for expansion work, since ΔU is the larger term in our equation.

I hope this helps you understand how to approach this problem. Remember, in science, it is important to start with the fundamental principles and equations, and then substitute in values as needed to solve the problem at hand.
 

1. What is a diatomic ideal gas?

A diatomic ideal gas is a theoretical model used in thermodynamics and statistical mechanics to describe the behavior of gases that consist of two atoms bonded together. Examples of diatomic gases include oxygen (O2), nitrogen (N2), and hydrogen (H2).

2. What properties does a diatomic ideal gas have?

A diatomic ideal gas is characterized by several properties, including volume, pressure, temperature, and number of moles. It follows the ideal gas law, which states that the product of pressure and volume is directly proportional to the product of temperature and number of moles.

3. How does a diatomic ideal gas differ from a monatomic ideal gas?

A monatomic ideal gas consists of single atoms, while a diatomic ideal gas consists of two atoms bonded together. This difference affects the behavior of the gases, with diatomic gases having higher heat capacities and being able to undergo phase changes at lower temperatures.

4. What is the significance of the term "ideal" in diatomic ideal gas?

The term "ideal" in diatomic ideal gas refers to the assumptions made in the model. These include negligible volume of the gas particles, no intermolecular forces, and elastic collisions. These assumptions make the calculations easier and provide a good approximation for real gases under certain conditions.

5. What are some real-life applications of diatomic ideal gases?

Diatomic ideal gases have various applications in fields such as chemistry, physics, and engineering. They are used to understand the behavior of real gases, determine the energy and entropy of chemical reactions, and calculate the efficiency of heat engines. They are also used in the design of refrigeration systems and gas laws experiments.

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