# Change in temprature is zero. what about change in internal energy?

• vkash
In summary, the change in internal energy is a function of temperature and is not always zero even if there is no change in temperature. In thermodynamic processes, both isothermal and adiabatic processes must be considered in order to accurately calculate the change in internal energy. Additionally, the concept of internal energy being solely dependent on temperature applies only to ideal gases and not to real gases.
vkash
change in internal energy is a function of temperature. So if there is no change in temperature then there should no change in internal energy.
But consider this example.
A gas is at 20 atm pressure in a room whose pressure is 1 atm.using external forces(on piston). Gas slowly expands its volume till it's pressure became 1 atm.during the process the temperature is maintained at 278K(room temperature).
work done in process
work done(W)= nRT*ln(P1/P2) (Δ)T=0; so it's isothermal)
heat supplied(Q)=0 (No heat is supplied, gas expand by force on piston of it's own pressure)
change in internal energy=Q-W (using Q=U+W)
So from here we come to know that change in internal energy is not zero. But there is no change in temperature during the whole process so change in internal energy should zero...
So where am i getting it wrong.?

thanks!

you will need to understand one of the basics in such contrived thermodynamic questions - isothermal (ie same temperature) and adiabatic (ie same energy) processes - in your example the internal energy changed because heat 'leaked out' into the room - overall energy was conserved

sambristol said:
you will need to understand one of the basics in such contrived thermodynamic questions - isothermal (ie same temperature) and adiabatic (ie same energy) processes - in your example the internal energy changed because heat 'leaked out' into the room - overall energy was conserved

I think you want to say that i am using both the processes in single case.(Q=0 as well as ΔT=0)
But what if we do this processes in a container having adiabatic walls(fully insulated walls). Will temperature of gas fall down?

yes - the kinetic energy of the escaped gas more than compensates for the specific heat capacity of the remaining gas* so it will cool - see footnote*

Regards

Sam

* Footnote This is for air at normal STP but all gases have an inversion temperature which is why we can liquidfy gases - look up Joule Kelvin Cooling

As they said, you can't consider there isn't heat exchange because in order to maintain the same temperature, you must exchange heat.

Also, internal energy is a function of temperature only if we are talking about ideal gases. This property does not hold for real gases.

## 1. What is the difference between change in temperature and change in internal energy?

The change in temperature refers to the difference in the average kinetic energy of particles in a system, while the change in internal energy refers to the total energy of a system, including both kinetic and potential energy.

## 2. Can the change in internal energy be zero while the change in temperature is not?

Yes, it is possible for the change in internal energy to be zero if there is no change in the potential energy of the system. However, the change in temperature can still be non-zero if there is a change in the kinetic energy of the particles.

## 3. How is the change in internal energy related to the heat transferred?

The change in internal energy is directly related to the heat transferred into or out of the system. This can be represented by the equation ΔU = Q - W, where Q is the heat transferred and W is the work done on or by the system.

## 4. Can the change in temperature and change in internal energy be negative?

Yes, both the change in temperature and change in internal energy can be negative if the system is losing heat and/or work is being done on the system. This indicates a decrease in the total energy of the system.

## 5. How does the change in internal energy affect the state of a system?

The change in internal energy can cause a change in the state of a system, such as a phase change from solid to liquid. This is because a change in internal energy can affect the intermolecular forces and arrangement of particles in a system.

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