How Does Doubling Internal Energy Affect Pressure in a Sealed Container?

In summary, in this conversation, the topic of pressure and internal energy is discussed in relation to a given problem. It is stated that pressure is independent of internal energy and will remain unchanged if the volume changes isothermally. However, if the volume stays the same and internal energy is increased, the temperature will also increase and the pressure may change depending on whether the gas is ideal and following the ideal gas law.
  • #1
ab94
11
0

Homework Statement


For example in the problem if we have a volume of 10L at 15 degrees Celsius, and there is initially 100Pascals pressure, what would the final pressure be if we double the Internal Energy?


Homework Equations


U=3/2nRT


The Attempt at a Solution


I though pressure was independent of Internal Energy so it would remain unchanged? but Idk
 
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  • #2
ab94 said:
I thought pressure was independent of Internal Energy so it would remain unchanged? but Idk
If you change the volume, and hence the pressure, isothermally then the internal energy will not change. But if the volume stays the same then pressure and temperature can only vary if the other does too. Here, internal energy is being increased, so the temperature is going up, but the volume stays the same. So what happens to the pressure?
 
  • #3
The pressure would also double?
 
  • #4
ab94 said:
The pressure would also double?
It depends. Is this an ideal gas? Can you explain your answer in terms of the ideal gas law?

AM
 
  • #5


As a scientist, you are correct in thinking that pressure is not directly affected by internal energy. However, there are other factors that can influence pressure, such as temperature and volume. In this problem, the volume and temperature are held constant, so the only variable that can change is the number of moles (n) in the system.

If we double the internal energy, it means that the number of moles in the system has also doubled. Using the ideal gas law, PV = nRT, we can rearrange it to solve for pressure (P):

P = nRT/V

Since the volume and temperature are constant, we can rewrite the equation as:

P = (2n)RT/V

This shows that the pressure will also double, from 100 Pascals to 200 Pascals. So the final pressure would be 200 Pascals.

In summary, while internal energy does not directly affect pressure, it can indirectly influence it through other variables such as the number of moles in the system.
 

FAQ: How Does Doubling Internal Energy Affect Pressure in a Sealed Container?

1. What is the difference between internal energy and pressure?

Internal energy is the total energy of a system, including both its kinetic and potential energy. Pressure, on the other hand, is a measure of the force per unit area exerted by a gas or liquid on its surroundings. In other words, internal energy refers to the energy contained within a system, while pressure refers to the force exerted by the system.

2. How are internal energy and pressure related?

Internal energy and pressure are closely related, as both are affected by the temperature and volume of a system. An increase in temperature will lead to an increase in internal energy, which in turn can increase the pressure of a gas or liquid. Similarly, a decrease in volume can also increase pressure, as the same amount of energy is now contained in a smaller space.

3. Can internal energy and pressure be changed independently?

Yes, internal energy and pressure can be changed independently of each other. This is because they are affected by different factors, such as temperature and volume, which can be altered separately. However, changes in one can still impact the other, as explained in the previous answer.

4. How is internal energy and pressure measured?

Internal energy is typically measured in joules (J) or calories (cal), while pressure is measured in units of force per unit area, such as pascals (Pa) or atmospheres (atm). These measurements can be obtained through various experimental techniques and calculations.

5. What are some real-world applications of understanding internal energy and pressure?

Understanding the relationship between internal energy and pressure is crucial in many scientific and engineering fields. For example, it is used in the design and operation of engines and turbines, as well as in the study of atmospheric conditions and weather patterns. It is also important in the field of thermodynamics, which is essential for the development of energy-efficient technologies and processes.

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