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

Name: Problem 87, Chapter 1: Problems and Solutions on Thermodynamics and Statistical Mechanics
Uploaded: 2023-11-21T15:37:00-08:00
Duration: 2 min 32 s
Channel: Nicholas Mogoi
Description: 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 entropy of the resistor? (b) What is the change in the entropy of the universe? (c) What is the change in the internal energy of the universe? (d) What is the change in the Helmholtz free-energy of the universe?

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 entropy of the resistor? (b) What is the change in the entropy of the universe? (c) What is the change in the internal energy of the universe? (d) What is the change in the Helmholtz free-energy of the universe?

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 entropy of the resistor?
(b) What is the change in the entropy of the universe?
(c) What is the change in the internal energy of the universe?
(d) What is the change in the Helmholtz free-energy of the universe?

Key Concepts

Joule Heating

Joule heating refers to the process by which electrical energy is converted into thermal energy as current passes through a resistor. This conversion is governed by the relation Q = I²Rt, where Q is the energy dissipated, I is the current, R is the resistance, and t is the time. It is a fundamental concept when analyzing how electrical systems generate heat and how this affects subsequent thermodynamic calculations.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout. In many practical situations, such as the resistor held at a constant temperature in this problem, any generated heat is immediately exchanged with the surroundings, ensuring that the system's temperature does not change, even though energy is continuously being converted or transferred.

Entropy

Entropy is a measure of the disorder or randomness in a system, and its change is used to quantify the irreversibility of processes. When heat is transferred at a constant temperature, the change in the entropy of a system is given by ?S = Q/T. In irreversible processes like Joule heating, entropy is produced both in the system and the surroundings, leading to an overall increase in the entropy of the universe.

Internal Energy

Internal energy is the total energy contained within a system, encompassing both kinetic and potential energy at the microscopic level. In an isothermal process, where the temperature is held constant, the net change in a system's internal energy is typically zero because any energy added as heat is balanced by work done on or by the system. This concept is crucial when applying the first law of thermodynamics.

Helmholtz Free Energy

Helmholtz free energy, defined as F = U - TS, is a thermodynamic potential that indicates the amount of work a system can perform at constant temperature and volume. Changes in Helmholtz free energy are especially important in isothermal conditions because a decrease in F signals an increase in the system’s ability to do work. In contexts involving energy dissipation and entropy production, such as Joule heating, the change in Helmholtz free energy helps quantify the system’s departure from equilibrium.

Transcript

Please give Ace some feedback