A system does 213 J of work on its environment and gains 77.8 J of heat in the process. Find the change in the internal energy of (a) the system and (b) the environment.

a) Change in internal energy of the system = - 135.2 J

b) Change in internal energy of the environment = 135.2 J

Explanation:

From the mathematical statement of the first law of thermodynamics,

ΔU = Q - W

ΔU = Change in internal energy of the system = ?

Q = heat transferred into or out of the system. For this system, heat is transferred into it, Q = 77.8 J

W = workdone = 213 J (positive because work is done by the system on the environment)

ΔU = 77.8 - 213 = - 135.2 J

The change in internal energy of the environment is just the negative of that of the system. The balance is always so.

Hence, change in internal energy of the environment = - ( - 135.2) = 135.2 J