A 100-ohm resistor is held at a constant temperature of 300 K. A current of 10...

A 100-ohm resistor is held at a constant temperature of 300 K. A current of 10 amperes is passed through the resistor for 300 sec.

a) What is the change in the internal energy of the universe?

b) What is the change in the Helmholtz free-energy of the universe?

Solutions

Expert Solution

a) The change in internal energy is
U = Q + W
Where Q is the change in heat energy and W is the work done.
The change in internal energy of the universe is equal to the change in heat energy of the universe since the work done is zero.
U = Q
When the current is passed through the resistor, joules heating effect happens and the energy released to the universe is
Q = I² R t
Where I is current, R is the resistance and t is the time for which the current is passed.
U = I² R t = 10² x 100 x 300 s
U = 3 x 10⁶ J
b) The Helmholtz free energy is
F = U - TS
Where S is the change in entropy of the universe.
The entropy change of the universe,
S = Q / T
F = U - T x ( Q / T)
F = U - Q = 3 x 10⁶ J - 3 x 10⁶ J = 0
F = 0
The change in Helmholtz free energy is zero.

genius_generous answered 1 year ago

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