Deriving an expression for change in internal energy

In summary, the conversation discusses the derivation of an expression for the difference in internal energy of an ideal gas that undergoes an irreversible process involving heat and work. The initial and final temperatures and volumes are given, and the number of moles is calculated using the ideal gas law. The relationship between internal energy and temperature is also mentioned, and it is determined that the change in internal energy per mole can be calculated using the initial and final temperatures.
  • #1
Krisd98
7
0
Homework Statement
A quantity of ideal gas initially at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work derive an expression for the difference in the internal energy of the gas
Relevant Equations
du=nc_vdt
Homework Statement: A quantity of ideal gas initially at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work derive an expression for the difference in the internal energy of the gas
Homework Equations: du=nc_vdt

I started of by finding the number of moles using this equation : PV=nRT. I found n=0.802.
I then found the final temperature from this equation: (P_1V_1/nRT_1)=(P_2V_2/nRT_2) and by rearanging found T_2=750K.
I have now constructed a pressure versus volume diagram to calculate the work and change in internal energy.
In the first it the volume is conatant so there's no work done so the internal energy is : change in U=Q
In the second bit the process is isothermal therefore the internal energy =0 but there is work done and Q=+.
Im unsure how to derive an expression for this could someone give me a little hint please
 
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  • #2
How is the internal energy of an ideal gas related to temperature?
 
  • #3
Chestermiller said:
How is the internal energy of an ideal gas related to temperature?

dU=nC_vdT or dU=Q+W
 
  • #4
Krisd98 said:
dU=nC_vdT or dU=Q+W
From the first equation, if you know the initial and final temperatures, don't you know the change in internal energy per mole?
 
  • #5
Chestermiller said:
From the first equation, if you know the initial and final temperatures, don't you know the change in internal energy per mole?

So i would have dU=0.8*5/2*8.314*750-300)
 
  • #6
Chestermiller said:
Yes. Please use delta’s and not d’s.
 

1. What is the definition of internal energy?

Internal energy refers to the total energy contained within a system, which includes the kinetic and potential energies of its particles. It is a state function, meaning it only depends on the current state of the system and not the path taken to reach that state.

2. Why is it important to derive an expression for change in internal energy?

Deriving an expression for change in internal energy allows us to understand how the internal energy of a system changes in response to different factors such as temperature, pressure, and volume. This information is crucial in many scientific fields, including thermodynamics, chemistry, and physics.

3. What is the formula for change in internal energy?

The formula for change in internal energy is ΔU = Q - W, where ΔU represents the change in internal energy, Q represents the heat added to the system, and W represents the work done on the system. This formula is based on the first law of thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system.

4. How can we use this expression to calculate the change in internal energy?

To calculate the change in internal energy, we need to know the amount of heat added to the system and the work done by the system. These values can be determined through experiments or by using other relevant equations. Once we have these values, we can plug them into the formula ΔU = Q - W and calculate the change in internal energy.

5. What factors can cause a change in internal energy?

There are several factors that can cause a change in internal energy, including changes in temperature, pressure, and volume, as well as adding or removing heat and doing work on the system. Any process that involves a transfer of energy to or from the system can result in a change in its internal energy.

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