A building-envelope concept uses a low-conductivity insulation layer and a sealed double-glazed cavity. Explain which mechanisms each measure primarily targets and why a complete design still requires all relevant paths.

A hot body and a cold body form an isolated composite system and are placed in thermal contact. Explain the spontaneous direction of energy transfer and the sign of the total entropy change.

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 $k = 0.84 \text{ W/(m}\cdot\text{K)}$. Treat the glass as one-dimensional steady conduction with its two surface temperatures maintained at $22^\circ\text{C}$ and $-5^\circ\text{C}$. What is the conductive heat-transfer rate through the glass?

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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.

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$2.0 \text{ moles}$ 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? ($R = 8.314 \text{ J/(mol}\cdot\text{K)}$)

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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?

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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?

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