## UY1: Heat is a path variable

The heat input to a system changing from an initial state i to a final state f depends on the path the system takes between these two states. Consider the following thought experiment, in which the initial states and final states are identical. Hence, the change in internal energy is zero. Isothermal gas expansion An ideal gas is confined in …

## UY1: Work is a path variable

The work output from a system changing from an initial state i to a final state f depends on the path the system takes between these two states. Consider the following three thought experiment, in which all initial states and all final states of the system are identical and at the same temperature, but the path taken to go from …

## UY1: Work output by gas pistons

In engines, a gas is often employed to perform work through gas expansion or pressure-volume work. Infinitesimal work output by the gas for an infinitesimal piston displacement dy is given by: \begin{aligned} dW_{\text{out}} &= F \, dy \\ &= PA \, dy \\ &= P \, dV \end{aligned} , where F is the force exerted by the gas on the …

## UY1: Definition and concepts of thermodynamics

Thermodynamics is the study of the flow and transformation of energy. Historically, thermodynamics was developed to understand how to make steam engines more efficient. Therefore, a distinction was made between the two forms of energy, heat and work, and the central question to be addressed was how to transform a larger fraction of heat into work. Heat (Q): The energy …

## UY1: Heat Capacity Of Solids

The molar specific heats of solids are often strongly temperature dependent. Generally, they decrease in a non-linear manner with decreasing temperature and approach zero as the temperature approaches absolute zero. This is explained by quantum theory as the result of more and more vibrational modes becoming “frozen in” and can no longer absorb energy. At sufficiently high temperatures, the molar …

## UY1: Crisis for equipartition theorem

Historical note: Crisis for the equipartition theorem at the end of the 1800s. The prediction of the equipartition theorem does not agree with the measured heat capacity of gases. Boltzmann: Defended the derivation of his equipartition theorem as correct, but suggested that gases might not be in thermal equilibrium. Lord Kelvin: Suggested that the derivation for the equipartition theorem must …

## UY1: Heat Capacity Of Gases

The heat input (Q) required to raise the temperature of n moles of gas from T1 to T2 depends not only on ΔT but also on how the pressure and volume of the gas are changed.   There are two important heat capacities: Heating or cooling at constant volume: Qv = nCvΔT, where Cv is the molar heat capacity at …