Zeroth & First Law of Thermodynamics Think of the Laws of Thermodynamics as the 'House Rules' for the energy of the universe. The First Law is the 'No Free Lunch' rule: energy cannot be created or destroyed, only transformed. It's like a bank account where every penny (Joule) must be accounted for—if you withdraw money (do work), your balance (internal energy) drops unless you deposit more (add heat). The Second Law is the 'Taxman' rule: every time you convert energy, nature takes a 'tax' in the form of disorder (entropy). You can never break even because heat naturally wants to spread out from hot to cold, making useful energy less available over time. The Third Law simply states you can't quit the game: you can never cool a system down to absolute zero to stop all motion. Zeroth & First Law of Thermodynamics Temperature tells us which way heat would flow if two bodies were put in contact. The Zeroth Law builds the very idea of temperature: if body A is in thermal equilibrium with body C, and B is also in equilibrium with C, then A and B are in equilibrium with each other. This equivalence allows a thermometer to act as the 'third body' C and assign a single reading called temperature to any system. Once temperature exists as a state property, the First Law gives the accounting rule for energy transfers: any heat supplied to a system either raises its internal energy or leaves as work done by the system. In Physics sign convention we use U = Q - W , where Q is heat added to the system (positive when absorbed) and W is the work done by the system on the surroundings (positive in expansion). For ideal gases, internal energy depends only on temperature, so U = n C v T . The work in a quasi-static process is the area under the P – V curve: W = P ,dV . Different processes (isothermal, adiabatic, isobaric, isochoric) produce different Q , W , and U , and recognizing which formula applies is the key to fast NEET solving. Crowded dance floor analogy: total people ≈ energy (First Law — count stays conserved), and neat choreography decays to a messy crowd unless guided (Second Law — entropy rises). remember Core vocabulary Thermodynamic system The part of the universe we choose to study. Can be a gas in a cylinder, a cup of tea, or a living cell. Surroundings Everything outside the system that can exchange energy or matter with it. Boundary Real or imaginary surface separating system and surroundings; may be fixed or movable, diathermic (allows heat) or adiabatic (blocks heat). Thermal equilibrium No net heat flow across a diathermic boundary when two bodies are in contact. Temperature A scalar state property that is equal for systems in mutual thermal equilibrium; measured in Kelvin ( K ). A property that depends only on the current state (e.g., P , V , T , U ), not on the path taken. State variable (state function) A quantity whose value depends on the process path, e.g., heat Q and work W . Path variable (process variable) Internal energy U Total microscopic kinetic and potential energies of molecules. For an ideal gas, U depends only on T . A process that proceeds infinitely slowly through a sequence of equilibrium states; needed for W = P ,dV to be valid. Quasi-static process Sign convention (Physics) Heat added to the system Q>0 ; work done by the system W>0 ; hence U = Q - W . Right after defining temperature via the Zeroth Law, the thermometer becomes our trusted third system. When two bodies show the same thermometer reading, they are in thermal equilibrium and there is no net heat flow between them if connected by a diathermic wall. This gives an operational way to compare temperatures and to build consistent scales like the Kelvin scale where 0 , K is the extrapolated absolute zero. In real life, we check fever with a thermometer exactly for this reason: the device equilibrates with your body and reports a number that is meaningful only because the Zeroth Law guarantees transitivity of equilibrium. First Law: the energy accounting rule First Law (finite change) Physics sign convention: W is work done by the system. First Law (infinitesimal) Exact differential for U ; Q and W are inexact (path-dependent). The change in a system's internal energy depends on the heat added and the work done by the system. Work in a quasi-static process Area under the P – V curve; positive for expansion. For a gas undergoing quasi-static expansion, this integral calculates the mechanical work done by the system against the external pressure. Internal energy of ideal gas U depends only on temperature for an ideal gas. For ideal gases, this relationship shows that internal energy change depends only on the temperature change, simplifying the First Law application. The First Law splits any added heat into two parts: a stored part as internal energy and an exported part as mechanical work. For gases the exported part shows up as piston motion against an external pressure. Because U is a state function, the change U from state 1 to 2 is independent of path. But Q and W depend on the route on the P – V plane. For cyclic processes the system returns to the same state, so U = 0 and the net heat absorbed equals net work done over the cycle. Do not mix Chemistry and Physics sign conventions. We use U = Q - W with W positive for work done by the system. Many Chemistry books write U = Q + W (with W as work done 'on ' the system). neet-alert tip Always convert temperatures to Kelvin when using gas laws or Carnot efficiency. Celsius differences can be used for T but not in ratios like T sink /T source . Standard processes and what First Law predicts Quick identities (ideal gas, quasi-static): Isothermal ( T=0 ): U=0 , so Q=W = nRT ! ( V 2 V 1 ) Adiabatic ( Q=0 ): U = -W , and PV = constant Isochoric ( V = 0 ): W=0 , so Q= U = n C v T Isobaric ( P= constant ): W=P V = nR T , and Q = n C p T Isothermal implies U=0 only for an ideal gas. For real gases, U can change with volume even at constant temperature. neet-alert Valid for ideal gases; R = 8.314 , J ,mol -1 ,K -1 . Mayer's relation For ideal gases, this relation provides a fundamental link between the heat capacities measured at constant pressure and constant volume. Adiabatic state equation = C p/C v . Curve is steeper than isotherm. A P – V diagram is your best friend. The work equals the signed area under the process curve. For a reversible isothermal expansion of an ideal gas from V 1 to V 2 , the P – V path is a rectangular hyperbola and the area evaluates to nRT (V 2/V 1) . For a reversible adiabatic expansion, the curve falls more steeply because no heat enters to compensate the energy exported as work; temperature therefore decreases and U drops. In an isochoric heating, the vertical line implies zero area (no work), so all the supplied heat raises U . pv m 3 Volume Start state P1 V1 V2 End isothermal P2 (isotherm) End adiabatic P2' (adiabat) V2 PV diagram comparing reversible isothermal and adiabatic expansions from the same start. Both curves start at the same initial state. The adiabatic curve drops faster than the isothermal as volume increases. Pressure Pa Isothermal dependent Adiabatic dependent Isothermal Q = nRT ln(V2/V1) W = nRT ln(V2/V1) PV = nRT at constant T Adiabatic (rev.) W = (P1 V1 - P2 V2)/(γ - 1) ΔU = -W PV γ = constant; TV γ-1 = constant Isochoric Q = n C v ΔT ΔU = n C v ΔT V = constant Isobaric Q = n C p ΔT W = nR ΔT ΔU = n C v ΔT P = constant Process Heat Q Work W ΔU Key equation (ideal gas) tip Boundary cases: as V 0 , ideal-gas model fails long before the pressure would diverge; as V , P 0 and work in further expansion approaches zero. Heat capacity ratio = C p/C v ; for ideal gases, C p - C v = R and > 1 . Reversible adiabatic process of an ideal gas obeys P 1 V 1 = P 2 V 2 . Efficiency of any heat engine: = 1 - Q sink /Q source . Maximum possible (Carnot) efficiency: = 1 - T sink /T source with temperatures in Kelvin. COP of refrigerator: = Q cold /W in ; often >1 . Define enthalpy. Differentiate. Definitions of heat capacities. Use ideal gas law. Substitute into the differential for H. Mayer's relation (per mole). Define adiabatic index. C p - C v = R, = C p/C v Mayer's relation and definition of γ Ideal gas Heat capacities independent of temperature over small range Quasi-static changes First Law with Q=0 . For ideal gas dU = nC v ,dT and W = P ,dV . Ideal gas law. Substitute for P. Use = C p/C v and C p-C v=R . Integrate both sides. Integrals of 1/x. Combine with PV=nRT . P 1 V 1 = P 2 V 2 Adiabatic state equation Ideal gas Reversible adiabatic process ( Q = 0 ) Quasi-static so that P is well-defined along path Efficiency of a heat engine Cyclic operation so U cycle =0 Heat absorbed from a hot reservoir Q source and rejected to a sink Q sink = 1 - Q sink Q source First Law over a cycle. Define thermal efficiency. Substitute W net . Carnot efficiency Reversible Carnot cycle between temperatures T source and T sink Isothermal and adiabatic steps are reversible = 1 - T sink T source For reversible processes, heat ratio equals temperature ratio. Engine efficiency definition. Substitute reversible ratio. First Law over one cycle. Define coefficient of performance. = Q cold W in COP of a refrigerator Cyclic refrigerator removing Q cold from cold space and rejecting Q hot to hot surroundings Work input W in drives the cycle Cutaway piston-cylinder showing blue and red particles, flame at base, and piston moving upward with temperature indicator. Heat engine model: a brass cylinder with a movable piston contains gas particles; heating at the bottom raises temperature and pushes the piston up. Entropy illustration: ordered cubes (low entropy) evolve into scattered shards (high entropy) along the arrow of time. Split panel showing neat stack of cubes on the left and shattered pieces dispersed on the right. Color map of a hot cup with warm plumes rising and a cool table surface beneath. Thermal image of a hot mug losing heat to cooler surroundings by conduction, convection, and radiation. Worked examples (linked to formulas) easy n = 2.0 mol T = 50 , K Constant volume (isochoric) Monatomic gas so C v = 3 2 R Use U = n C v T , and at constant volume W=0 , so Q= U . 2.0 mol of a monatomic ideal gas is heated at constant volume so that its temperature rises by 50 K. Find U , W , and Q . U , W , Q n = 1 mol T = 300 K V1 = 2.0 L = 2.0 10 -3 , m 3 V2 = 6.0 L = 6.0 10 -3 , m 3 medium Work W, Heat Q, Internal energy change ΔU 1 mol of an ideal gas expands isothermally at T=300 , K from 2.0 , L to 6.0 , L . Find W , Q , and U . Isothermal ideal gas: U=0 and W = nRT (V 2/V 1) ; by First Law, Q=W . Air ( =1.4 ) in a cylinder is compressed reversibly and adiabatically from P 1=1.0 10 5 , Pa , V 1=1.0 10 -2 , m 3 , T 1=300 , K to V 2=5.0 10 -3 , m 3 . Find T 2 , P 2 , and work done by the gas. T2, P2, W by system SI Use TV -1 = const for T 2 , PV = const for P 2 , and W = (P 1V 1 - P 2V 2)/( -1) for work by the system. γ = 1.4 P1 = 1.0× 10 5 Pa V1 = 0.010 m 3 V2 = 0.005 m 3 T1 = 300 K Reversible adiabatic (Q=0) hard neet-alert In adiabatic compression of an ideal gas, work is done on the gas, so W (by system) is negative and temperature rises. Many students wrongly set W=0 just because there is thermal insulation ( Q=0 ); the piston can still move and mechanical work can be exchanged. Heats, works, and energies in biology: a beating heart, an active neuron, and ATP hydrolysis all obey the First Law. In a closed cell compartment modeled as a system, heat from metabolism raises internal energy or is exported as mechanical work (muscle contraction, pressure-volume work in lungs). While microscopic details are complex, the macroscopic statement U = Q - W still tracks the energy bookkeeping. Q → U + Work: Think “Heat supplied either Ups the energy or does Work.” With Physics signs: Q = U + W so rearrange to U = Q - W . Heat is a state property, so the net heat in a cycle must be zero. Heat is path-dependent. In a cycle U=0 , but Q net equals the net work, which need not be zero. At equal Celsius readings, Carnot efficiency uses the same ratio. Temperatures in efficiencies and gas laws must be in Kelvin. Using Celsius in ratios leads to wrong answers. Practical checklists for process problems: 1) Identify the process (which variable is held constant or which transfer is blocked). 2) Write U = n C v T for ideal gases. 3) Pick the correct work expression: W= P ,dV , or W=0 for isochoric, or W = nRT (V 2/V 1) for isothermal, or W= P 1V 1 - P 2V 2 -1 for adiabatic (reversible). 4) Apply the First Law to solve for the unknown. Unit discipline and signs decide speed and accuracy. Pressures in Pa, volumes in m 3 , temperatures in K . Use R = 8.314 , J ,mol -1 ,K -1 . Keep two significant figures for NEET-style outputs unless specified. Indicate the sign of work clearly (by system vs on system). Unit discipline checklist Why C p > C v ? At constant pressure, when you supply heat the gas must expand to keep P fixed; part of the heat therefore leaves as work P V , leaving less to raise the temperature. So to achieve the same T you must supply more heat than at constant volume: C p - C v = R for ideal gases. This difference is behind = C p/C v , a number that controls how steeply an adiabat falls. Edge examples help intuition: If you insulate a gas perfectly and shake it violently, its temperature rises even though Q=0 . Mechanical agitation does work on the gas ( W<0 for work done by the system), so U = -W > 0 and T increases. Conversely, in free expansion into vacuum, P ext =0 so W=0 and for an ideal gas Q=0 (in a rigid, insulated container). Then U=0 and the temperature does not change — a classic NEET favorite. remember Free expansion of an ideal gas: W=0 , Q=0 , and U=0 so T stays constant even though P and V change. From engines to refrigerators, the First Law sets the energy budget, while the Second Law sets the direction and the ultimate limits. For an engine, Q source enters, some part emerges as useful work W , and the rest Q sink must be expelled. An idealized Carnot engine reaches the maximum possible efficiency at given reservoir temperatures, and no design can beat = 1 - T sink /T source . For a refrigerator, the desired output is not work but heat removal from the cold space. The coefficient of performance = Q cold /W in is often greater than 1 because the device moves heat rather than creating it. In a kitchen, when the fridge runs with the door open, the room warms overall since the motor’s work becomes extra heat released on the back side. When do popular formulas apply? Isothermal work W = nRT (V 2/V 1) requires an ideal gas and a reversible isothermal path. Adiabatic PV = constant requires an ideal gas, reversible adiabatic (no heat exchange) and constant heat capacities. Mayer’s relation C p - C v = R holds only for ideal gases; real gases deviate. Engine = 1 - Q sink /Q source is general for any cycle using positive magnitudes of heats. Worked sign drill: Suppose a gas at 300 , K expands and does 500 , J of work while its internal energy decreases by 200 , J . Then W=+500 , J (by system), U=-200 , J , so by First Law Q = U + W = -200 + 500 = +300 , J , meaning the gas absorbed 300 J of heat from the surroundings to partly support the expansion. Isothermal work (ideal gas, reversible) Determines the work done by an ideal gas undergoing expansion or compression while maintaining a constant temperature. Adiabatic work (reversible ideal gas) This equation determines the work done by a gas during an adiabatic process, where no heat is exchanged with the surroundings. Graph sense: On a P – V plot a clockwise loop indicates a heat engine because the enclosed area (net work) is positive — the system does work on surroundings. A counterclockwise loop indicates a refrigerator or heat pump where net work is done on the system to move heat opposite to its natural direction. Thermodynamic language precision: Q and W are not properties that the system 'has'; they are modes of energy transfer during a process. Only U , P , V , T , and similar variables describe the system’s state. Writing Q 1 , Q 2 for the 'heat content' of a state is meaningless; use internal energy U instead. Transitive property of thermal equilibrium; underlies temperature measurement. Zeroth Law Energy conservation for thermodynamic systems: U = Q - W . First Law Heat Q Energy transfer due to temperature difference; path-dependent. Work W Energy transfer by macroscopic forces; for gases W= P ,dV in quasi-static paths. Microscopic energy stored in the system; state function. Internal energy U Isothermal / Adiabatic / Isochoric / Isobaric Standard processes with T constant, Q=0 , V constant, P constant respectively. Ratio C p/C v controlling adiabatic curves. Adiabatic index Recap glossary