Which of the following is an intensive thermodynamic state variable?

In an adiabatic expansion of a monoatomic gas ($\gamma = 5/3$), which of the following is strictly true?

The efficiency of a Carnot Engine working between temperatures $600 \text{ K}$ and $300 \text{ K}$ is:

For a cyclic process traced in a clockwise direction on a P-V diagram:

Which physical law formally introduces the concept of internal energy ($U$)?

State the Zeroth law of thermodynamics and explain its significance in defining a common physical property.

Distinguish between a state function and a path function in thermodynamics, providing one example of each.

Explain conceptually why the molar specific heat of a gas at constant pressure ($C_p$) is strictly greater than its molar specific heat at constant volume ($C_v$).

State the Kelvin-Planck and Clausius statements of the Second Law of Thermodynamics.

Why does the sudden bursting of a high-pressure car tire make the escaping air instantly feel noticeably cold? Identify the specific thermodynamic process responsible.

Using the first law of thermodynamics and the ideal gas equation, rigorously derive Mayer's relation: $C_p - C_v = R$.

Derive an expression for the total work done ($W$) by $\mu$ moles of an ideal gas during an isothermal expansion from volume $V_1$ to $V_2$ at temperature $T$.

Show with mathematical proof that the slope of an adiabatic curve generated on a P-V indicator diagram is exactly $\gamma$ times steeper than the slope of an isothermal curve passing through the absolute same state point.

Draw a neatly labeled schematic block diagram of a Heat Engine. Further, express its efficiency ($\eta$) mathematically in terms of the heat absorbed from the source ($Q_1$) and the heat rejected to the sink ($Q_2$). Under what hypothetical condition can this efficiency reach 100%?

Draw the four precise strokes comprising a Carnot Cycle sequentially on a standard P-V indicator diagram. Clearly label each continuous curve with the name of the thermodynamic process it strictly represents.

An ideal heat engine operating on the Carnot cycle extracts heat from a source at $327^\circ \text{C}$ and rejects exhaust heat to a sink at $27^\circ \text{C}$. If the engine produces exactly $2 \text{ kJ}$ of useful mechanical work per cycle, determine:
(a) The thermal efficiency of the engine.
(b) The total amount of heat absorbed from the hot source per cycle.
(c) The net amount of heat deposited into the cold sink per cycle.

Exactly 4 moles of an ideal diatomic gas ($\gamma = 1.4$) initially at a temperature of $300 \text{ K}$ and an atmospheric pressure of $1 \text{ atm}$ are compressed adiabatically to exactly one-third ($1/3$) of their original volume. Calculate:
(a) The final temperature of the gas after compression.
(b) The exact final resultant pressure (in atm).
(c) The net quantity of mechanical work done during the process.

A thermodynamic active element undergoes a continuous cyclic process $A \to B \to C \to A$ as shown on a geometric P-V diagram. The given path coordinates are exactly: $A = (10 \text{ L}, 1 \times 10^5 \text{ Pa})$, $B = (30 \text{ L}, 1 \times 10^5 \text{ Pa})$, and $C = (10 \text{ L}, 4 \times 10^5 \text{ Pa})$. For this triangular cycle:
(a) Sketch the precise cycle correctly on a P-V graph axis.
(b) State whether net work is done by the gas or on the gas.
(c) Calculate the exact magnitude of the net work done over the complete thermodynamic cycle in Joules.

A room electrically powered air conditioner behaves fundamentally as a reverse heat pump (refrigerator) having a fixed Coefficient of Performance ($\alpha$) of precisely 3.5. If the machine continually extracts an internal energy amount of $7000 \text{ J}$ of heat sequentially from the cooler interior air per unit operational cycle:
(a) Calculate the compulsory electrical work magnitude delivered by the AC's motorized compressor per cycle.
(b) Determine the complete amount of heat continuously expelled back outwards into the warmer exterior environment per cycle.