AP Physics 2 PV diagrams cheat sheet

What does P stand for in PV diagrams?

P represents pressure, measured in Pascals (Pa) or atmospheres (atm).

What does V stand for in PV diagrams?

V represents volume, typically measured in liters (L) or cubic meters (m³).

What is the area under a PV curve?

The area under the curve represents the work done during the thermodynamic process.

Fill in the blank: In an isothermal process, temperature remains _____.

constant.

True or False: Isobaric processes occur at constant volume.

False - Isobaric processes occur at constant pressure.

Compare isochoric and isobaric processes.

Isochoric: constant volume, no work done. Isobaric: constant pressure, work done is PΔV.

What is an adiabatic process?

An adiabatic process occurs without heat exchange with the surroundings (Q = 0).

Cause → Effect: Increasing temperature in a gas at constant volume.

Effect: Pressure increases due to increased kinetic energy of molecules.

Equation for work done in an isobaric process?

Work done, $\displaystyle W = P imes riangle V$.

Describe isothermal expansion on a PV diagram.

Curve slopes downward; as volume increases, pressure decreases at constant temperature.

What does the slope of a PV curve indicate?

The slope indicates the relationship between pressure and volume: $\displaystyle \frac{dP}{dV}$.

What happens to a gas in an isochoric process?

No change in volume; pressure changes with temperature according to $\displaystyle P/T = ext{constant}$.

True or False: The first law of thermodynamics applies to all thermodynamic processes.

True - It relates changes in energy, heat, and work for any process.

Fill in the blank: In a cyclic process, the net change in internal energy is _____.

zero.

What is a phase transition shown in PV diagrams?

A flat line indicates a phase transition, where pressure remains constant as volume changes.

Example: Calculate work done in a process from (2L, 1atm) to (4L, 1atm).

Work done: $\displaystyle W = P imes riangle V = 1 ext{ atm} imes (4-2) ext{ L} = 2 ext{ atm·L}.$

Isothermal process → definition?

A process at constant temperature (T). Internal energy (U) remains constant. Work done (W) related to heat (Q) exchanged. Formula: $\displaystyle W = nRT ext{ln} \frac{V_f}{V_i}$.

Adiabatic process → characteristics?

No heat exchange (Q = 0). Changes in internal energy (U) equal work done (W). Formula: $\displaystyle W = \frac{P_f V_f - P_i V_i}{ ext{specific heat ratio}}$.

Calculate work in isobaric process: P = 2 atm, V_i = 10 L, V_f = 15 L.

Work done (W) is calculated as: $\displaystyle W = P imes riangle V$ Convert pressure to Pa (1 atm = 101325 Pa): $\displaystyle W = 202650 ext{ Pa} imes (15 - 10) imes 10^{-3} ext{ m}^3 = 1013.25 ext{ J}$.

True or False: Work done in isochoric process is zero.

True. In an isochoric process, volume remains constant, so no work is done (W = 0).

Determine signs of work: Expansion vs. Compression.

Expansion (W > 0): system does work. Compression (W < 0): work done on system.

What happens to internal energy in isothermal process?

Internal energy (U) remains constant. Heat (Q) added equals work done (W) by the system.

Heat added in adiabatic process → effect on temperature?

Temperature increases if heat is added. Reason: Work done by the system leads to energy transfer, altering temperature.

Work formula in terms of pressure and volume change?

Work can be expressed as: $\displaystyle W = ext{Area under PV curve} = ext{integral} ext{P} ext{dV}$.

Specific heat ratio (γ) → definition?

Ratio of specific heats: $\displaystyle γ = \frac{C_p}{C_v}$; affects work done in adiabatic processes.

Identify process: constant volume, no work done.

Isochoric process: Volume remains constant (ΔV = 0), hence W = 0.

Calculate work for isothermal expansion: T = 300 K, n = 1 mol.

Use $\displaystyle W = nRT ext{ln} \frac{V_f}{V_i}$; Assuming V_f = 2V_i: $\displaystyle W = (1 ext{ mol})(8.31 \frac{J}{K imes mol})(300 K) ext{ln} 2$.

Relation of work and heat in adiabatic process?

In an adiabatic process, Q = 0. Therefore, change in internal energy (ΔU) equals work done (W): $\displaystyle riangle U = W$.

Isothermal vs. Adiabatic: main difference?

Isothermal: T constant, Q exchanged. Adiabatic: no heat exchange (Q = 0), T changes.

Describe PV diagram for isobaric process.

Horizontal line on PV diagram. Pressure constant, volume changes. Work done equals area under the line.

Calculate work for adiabatic compression: V_i = 5 L, V_f = 2 L, γ = 1.4.

Use formula: $\displaystyle W = \frac{P_f V_f - P_i V_i}{γ}$; Estimate pressures using ideal gas law.

What does the area under a PV curve represent?

The area under the PV curve represents the work done during a thermodynamic process.

First Law of Thermodynamics

Energy cannot be created or destroyed, only transformed. - Implication: ΔU = Q - W, where ΔU = change in internal energy, Q = heat added, W = work done.

Second Law of Thermodynamics

Entropy of an isolated system always increases. - Implication: Heat flow is spontaneous from hot to cold.

True or False: Work done is always positive.

False. Work done by the system is positive; work done on the system is negative.

Third Law of Thermodynamics

As temperature approaches absolute zero, entropy approaches a minimum value. - Implication: No system can reach absolute zero.

Fill in the blank: In a PV diagram, isothermal processes are represented as _______ lines.

horizontal lines, indicating constant temperature.

PV diagram: Isobaric vs. Isochoric

Isobaric: constant pressure (horizontal line). Isochoric: constant volume (vertical line). - Work done: Isobaric has work; Isochoric has none.

Carnot Theorem

No engine operating between two heat reservoirs can be more efficient than a Carnot engine. - Efficiency: $$ext{Efficiency} = 1 - \frac{T_C}{T_H}$$

Implication of adiabatic processes

No heat exchange occurs. - PV relationship: $\displaystyle PV^\frac{ ext{γ}}{( ext{γ} - 1)} = ext{constant}$, where γ = Cp/Cv.

Define enthalpy.

Enthalpy (H) = U + PV. - Implication: Useful for processes at constant pressure.

Heat Engines Efficiency Formula

Efficiency = $\displaystyle \frac{W_{out}}{Q_{in}}$. - Represents the ratio of work output to heat input.

Comparison: Heat vs. Work

Heat: energy transfer due to temperature difference. Work: energy transfer due to force acting over a distance.

Fill in the blank: In adiabatic processes, __________ is constant.

internal energy change is equal to work done.

True or False: All thermodynamic processes are reversible.

False. Many real processes are irreversible, increasing entropy.

Relation between P, V, and T for ideal gas

Ideal gas law: $\displaystyle PV = nRT$. - Indicates how pressure, volume, and temperature relate.

Define specific heat capacity.

Specific heat (c) = heat added per unit mass per unit temperature change. - Formula: $\displaystyle Q = mcΔT$.

Fill in the blank: The area under the curve in a PV diagram represents __________.

the work done by or on the system.