Change in internal energy of a gas

In summary, the problem involves two moles of carbon monoxide (CO) starting at a pressure of 1.2 atm and a volume of 30 liters and being compressed adiabatically to 1/3 of the original volume. The gas can be treated as ideal and the change in internal energy is being sought. The relevant equations are Q = dU + W, dU = nCpdT - pdV, PV = nRT, and TV^{\gamma}= constant. However, dT is unknown and further calculations cannot be done without it. T_1 can be found using PV = nRT and T_2 can be found using the adiabatic equation.
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Homework Statement


Two moles of carbon monoxide (CO) start at a pressure of 1.2 atm and a volume of 30 liters. The gas is then compressed adiabatically to 1/3 this volume. Assume that the gas may be treated as ideal.

What is the change in the internal energy of the gas?

n = 1.2 atm
V2 = 10L
V1 = 30L
Cp = 29.16 J/(mol * K)

Homework Equations


Q = dU + W

The Attempt at a Solution


dU = dQ - dW
dU = nCpdT - pdV

dT is not known, and I can't go any further.
 
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  • #2
You can find [tex]T_1[/tex] using PV = nRT. You can then use the adiabatic equation [tex]TV^{\gamma}= constant [/tex] to find [tex]T_2[/tex]
 

FAQ: Change in internal energy of a gas

1. What is the definition of change in internal energy of a gas?

The change in internal energy of a gas refers to the difference between the initial and final internal energies of a gas. This can be caused by various factors such as temperature changes, pressure changes, and chemical reactions.

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

The change in internal energy of a gas can be calculated using the equation: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the gas, and W is the work done on the gas.

3. What factors can cause a change in internal energy of a gas?

There are several factors that can cause a change in internal energy of a gas, including changes in temperature, pressure, volume, and chemical reactions. These changes can result in an increase or decrease in the internal energy of the gas.

4. How does the change in internal energy affect the behavior of a gas?

The change in internal energy of a gas can affect its behavior in different ways. For example, an increase in internal energy can cause the gas molecules to move faster and increase the pressure of the gas. On the other hand, a decrease in internal energy can cause the gas molecules to move slower and decrease the pressure of the gas.

5. Can the change in internal energy of a gas be negative?

Yes, the change in internal energy of a gas can be negative. This indicates that the internal energy of the gas has decreased, which can happen when the gas releases heat or does work on its surroundings.

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