Find the final internal energy of a gas.

In summary, a thermally isolated container filled with 2.3 mol of an ideal gas at 0°C is compressed from 1.9 m3 to 0.3 m3 at constant pressure. The final internal energy of the gas can be calculated using the equation U=3/2nRT, where n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Since the process occurs at constant pressure, the work done is equal to the change in volume multiplied by the pressure (W=pΔV). The final internal energy is therefore U=-4398.6 J, which is equivalent to 1.24 kJ.
  • #1
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Homework Statement


A thermally isolated container is filled with 2.3 mol of an ideal gas at T = 0°C.The gas is then compressed from 1.9 m3 to 0.3 m3. What is the final internal energy U of the gas? (Assume the process occurs at constant pressure.)

Homework Equations


U=3/2nRT
U=Q+W
W=pΔV
pV=nRT


The Attempt at a Solution


Q=0, so U=W

p(1.9)=(2.3)(8.314)(273.15)
p(1.9)=5223.2
p=2749.1

W=pΔV
=(2749.1)(0.3-1.9)
=(2749.1)(-1.6)
=-4398.6

The actual answer is 1.24kJ.

I attempted this as well just to see.

U=3/2nRT
=3/2(2.3)(8.314)(273.15)
=7834.8

Clearly I am lost. Any help would be greatly appreciated.
 
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  • #2
Nevermind. I got it :D
 

1. What is the definition of internal energy?

The internal energy of a gas is the sum of all the microscopic forms of energy, such as the kinetic energy of its molecules and the potential energy from intermolecular forces.

2. How is the final internal energy of a gas calculated?

To find the final internal energy of a gas, you need to know the initial internal energy, the work done on or by the gas, and the heat added to or removed from the gas. The final internal energy is then the sum of the initial internal energy and the work and heat values.

3. What factors can affect the final internal energy of a gas?

The final internal energy of a gas can be affected by changes in temperature, pressure, and volume. It can also be influenced by the type of gas and the amount of work and heat added or removed from the system.

4. How does the first law of thermodynamics relate to the final internal energy of a gas?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. In the context of the final internal energy of a gas, this means that the total energy of the system (internal energy, work, and heat) remains constant.

5. Can the final internal energy of a gas ever be negative?

Yes, the final internal energy of a gas can be negative if work is done on the gas and heat is removed from the system. This means that the total energy of the gas has decreased, resulting in a negative value for the final internal energy.

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