A balloon is heated by adding 1000 J of heat. It expands by about 5 liters against a constant atmospheric pressure of 1 atm. Calculate the change in the internal energy of the system.
I. 1000 J heat is supplied to the system (balloon).
So, Q = + 1000 J
II. Balloon expands by a volume of 5.0 L.
So, work done by the system during expansion is given by-
W =- p dV
where, p = 1 atm = 1.01325 x 105 Pa
dV = 5.0 L = 5.0 x (10-3 m3) = 5.0 x 10-3 m3
Or, W = (1.01325 x 105 Pa) x (5.0 x 10-3 m3)
Or, W = 506.625 Pa m3
Or, W = 506.625 J ; [1 J = 1 Pa m3]
Note that, work is done by the system on surroundings.
Now, Change is internal energy of the system is given by first law of thermodynamics as follow-
dU = Q – W
where, dU = Change in internal energy
Q = Heat supplied to the system
W = Work done by the system.
Pitting the values from I and II in above equation-
dU = 1000 J – 506.625 J
Hence, dU = 493.375 J = + 493.375 J
A positive value of dU indicates that there is net gain of heat by the system during the overall process (heat supply and expansion).