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

[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!

 

[sambristol]

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

 

[vkash]

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?

 

[sambristol]

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

 

[Hobold]

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.