Adiabatic and Isothermal work

These flashcards cover crucial vocabulary and concepts related to constant and variable pressure work in thermodynamics, including equations, definitions, and implications of different processes.

Constant Pressure Work

Work done by a system at constant external pressure, calculated as W = -PΔV.

Variable Pressure Work

Work done by a system when pressure changes during the process, calculated using integration.

Ideal Gas

A hypothetical gas whose molecules occupy negligible space and have no interactions, used to model behavior in thermodynamics.

Work Equation for Constant Pressure

W = -PΔV.

Work done during Expansion

When a gas expands, the work done can be overestimated if the pressure change is not accounted for.

Work done during Compression

When a gas compresses, the work done can be underestimated if only the initial pressure is used.

Integration in Variable Pressure Work

Summing small slices to calculate work when pressure is not constant, represented by an integral.

First Law of Thermodynamics

The principle stating that the change in internal energy is equal to the sum of heat added and work done.

Adiabatic Process

A process in which no heat is transferred to or from the system.

Isothermal Process

A process in which temperature remains constant.

Internal Energy (ΔU) for Ideal Gases

ΔU is only dependent on temperature, given by ΔU = nC_VΔT.

Equation for Adiabatic Work

C_V log(T2/T1) = -R log(V2/V1).

Boyle's Law

The principle stating that P1V1 = P2V2 for a gas under constant temperature.

Adiabatic Variation of Boyle's Law

P1V1^γ = P2V2^γ, accounting for adiabatic processes.

Molar Heat Capacity at Constant Volume (C_V)

The amount of heat required to raise the temperature of one mole of a substance by one degree at constant volume.

Molar Heat Capacity at Constant Pressure (C_P)

The amount of heat required to raise the temperature of one mole of a substance by one degree at constant pressure.

Ratio of Heat Capacities (γ)

Defined as γ = CP/CV, describes how heat capacity changes under different conditions.

Integration Limits in Work Calculation

Work is calculated as negative integral from initial to final volume.

Final Temperature Calculation Formula

T2 = (P2V2)/(nR), used in ideal gas calculations.

Change in Enthalpy Formula

ΔH = nC_PΔT, used for calculating enthalpy changes.

Constant Pressure Work Example

A gas expands from 5\text{ L} to 10\text{ L} against a constant external pressure of 2\text{ atm}. Calculate the work done. W = -P\Delta V = -(2\text{ atm}) (10\text{ L} - 5\text{ L}) = -10\text{ L}\cdot\text{atm} (\text{Note: } 1\text{ L}\cdot\text{atm} \approx 101.325\text{ J})

Internal Energy Change Example (Ideal Gas)

Two moles of an ideal gas are heated, causing the temperature to rise by 10\text{ K}. If the molar heat capacity at constant volume (CV) for the gas is 12.5\text{ J/(mol}\cdot\text{K}), calculate the change in internal energy (\Delta U). \Delta U = nCV\Delta T = (2\text{ mol}) (12.5\text{ J/(mol}\cdot\text{K})) (10\text{ K}) = 250\text{ J}

Adiabatic Process Example

An ideal gas with \gamma = 1.4 at an initial pressure of 100\text{ kPa} and volume of 2\text{ L} undergoes an adiabatic expansion to 4\text{ L}. What is the final pressure? P1V1^\gamma = P2V2^\gamma \implies (100\text{ kPa})(2\text{ L})^{1.4} = P2(4\text{ L})^{1.4} P2 = (100\text{ kPa}) (2/4)^{1.4} = (100\text{ kPa}) (0.5)^{1.4} \approx 37.89\text{ kPa}

Enthalpy Change Example

Three moles of a gas are cooled, causing the temperature to drop by 15\text{ K}. If the molar heat capacity at constant pressure (CP) is 20.8\text{ J/(mol}\cdot\text{K}), calculate the change in enthalpy (\Delta H). \Delta H = nCP\Delta T = (3\text{ mol}) (20.8\text{ J/(mol}\cdot\text{K})) (-15\text{ K}) = -936\text{ J}