How Is Heat Distribution Calculated in a Diatomic Ideal Gas Expansion?

[wowolala]

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= $$\frac{7}{2}$$ 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

 

[Nate810]

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.

 

[Moetasim]

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.