Question

Two containers, A and B, contain equal amount of the same ideal gas occupying the same volume, and at the same temperature initially. Container A is fitted with a moveable piston, while volume of container B is fixed. Then equal amount of heat is added to both systems. When heat is added to container A, it expands. How do the final temperatures of the two systems compare and why?

a) System A has a final higher temperature than B due to the difference in internal energy consupmtion in system A's expansion

b) System A has a lower final temperature than B due to the difference in internal energy consupmtion in system A's expansion

c) the two systems have the same final temperatue since they habe the same initial temperature and the same mass and equal amount of heat is added to them

d) system A has a higher final temp the difference is due to the interal energy gain in system A's expansion

e) system A has a lower final temp the difference is due to the interal energy gain in system A's expansion

Answer 1

in first container:

heat supplied=change in internal energy+work done by the gas in expanding

so change in internal energy=heat supplied-work done

where work done is positive as the gas is expanding.

in second container

as there is no volume change, work done=0

then change in internal energy=heat supplied

so change in internal energy of the gas in container B is greater than change in interna energy

of the gas in container A.

as change in internal energy is directly proportional to change in temperature

so system B has a final higher temperature than system A

hence option B is correct.