A significant portion of energy consumed in modern societies goes toward heating and cooling buildings. Engineers use thermodynamics to minimize unwanted heat transfer. To combat conduction through walls, they use materials with low thermal conductivity ($k$), like fiberglass or foam. To reduce convection, they use double-paned windows filled with argon gas; the small space prevents significant convective currents from forming. Minimizing heat transfer ($Q/t$) directly translates into massive energy and cost savings over the lifetime of a structure.

The Second Law of Thermodynamics states that the total entropy ($\Delta S$) of an isolated system always increases. The universe itself is the ultimate isolated system. Every time a star burns, a galaxy forms, or a person breathes, energy is converted from concentrated, useful forms (like nuclear or chemical energy) into diffuse, unusable thermal energy (heat). This relentless increase in entropy implies that eventually, the universe will reach a state of maximum entropy—a uniform, cold temperature where no more work can be done and no life can exist, often referred to as the "Heat Death."

A single-pane glass window has an area of $2.0 \text{ m}^2$, a thickness of $0.005 \text{ m}$ (5 mm), and a thermal conductivity of $k = 0.84 \text{ W/(m}\cdot\text{K)}$. If the inside temperature is $22^\circ\text{C}$ and the outside temperature is $-5^\circ\text{C}$, what is the rate of heat loss through the window?

The surface temperature of the Sun is approximately $5800 \text{ K}$, and its radius is $6.96 \times 10^8 \text{ m}$. Assuming the Sun acts as a perfect blackbody (emissivity $e=1$), calculate the total power radiated by the Sun into space. ($\sigma = 5.67 \times 10^{-8} \text{ W/(m}^2\cdot\text{K}^4)$)

A $0.5 \text{ kg}$ block of hot iron ($c = 450 \text{ J/(kg}\cdot^\circ\text{C)}$) at $200^\circ\text{C}$ is dropped into an insulated copper calorimeter cup ($c = 385 \text{ J/(kg}\cdot^\circ\text{C)}$) of mass $0.2 \text{ kg}$ containing $1.0 \text{ kg}$ of water ($c = 4186 \text{ J/(kg}\cdot^\circ\text{C)}$) initially at $20^\circ\text{C}$. Find the final equilibrium temperature of the system.

In an engine cylinder, $500 \text{ J}$ of heat is added to a gas. The gas expands and does $300 \text{ J}$ of work on the piston. What is the change in the internal energy of the gas?

A gas in a cylinder with a movable piston expands from a volume of $0.02 \text{ m}^3$ to $0.05 \text{ m}^3$ at a constant pressure of $1.5 \times 10^5 \text{ Pa}$. Calculate the work done by the gas.

$2.0 \text{ moles}$ of an ideal gas expand isothermally (constant temperature) at $300 \text{ K}$ from an initial volume of $10 \text{ Liters}$ to a final volume of $30 \text{ Liters}$. How much work does the gas do? ($R = 8.314 \text{ J/(mol}\cdot\text{K)}$)

A car engine extracts $8000 \text{ J}$ of heat from burning gasoline in a cycle. It does $2400 \text{ J}$ of mechanical work per cycle. What is its thermal efficiency? How much heat is expelled to the exhaust?

A power plant operator claims to have invented an engine that takes in heat at $600\text{K}$ and exhausts it at $300\text{K}$ while achieving a thermal efficiency of $60\%$. Is this claim possible?

A kitchen refrigerator has a Coefficient of Performance ($COP$) of $4.0$. It needs to remove $12,000 \text{ J}$ of heat from the food compartment to keep it cool. How much electrical work (energy) must the compressor motor provide to do this? How much total heat is expelled into the kitchen room?