If the ratio of specific heat of a gas at Constant pressure...

If the ratio of specific heat of a gas at Constant pressure to that at constant volume is $\gamma$, the Change in internal energy of the mass of gas, when the volume changes from $\mathrm{V}$ to $2 \mathrm{~V}$ at Constant Pressure p, is (A) $\{(\mathrm{PV}) /(\gamma-1)\}$ (B) $\{\mathrm{R} /(\gamma-1)\}$ (C) PV (D) $\{(\gamma \mathrm{PV}) /(\gamma-1)\}$

If the ratio of specific heat of a gas at Constant pressure to that at constant volume is $\gamma$, the Change in internal energy of the mass of gas, when the volume changes from $\mathrm{V}$ to $2 \mathrm{~V}$ at Constant Pressure p, is
(A) $\{(\mathrm{PV}) /(\gamma-1)\}$
(B) $\{\mathrm{R} /(\gamma-1)\}$
(C) PV
(D) $\{(\gamma \mathrm{PV}) /(\gamma-1)\}$

Key Concepts

Ideal Gas Law

The ideal gas law, given by PV = nRT, relates the pressure, volume, and temperature of an ideal gas. It is fundamental in converting between volume changes and temperature changes in problems dealing with ideal gases, particularly when analyzing processes under constant pressure or constant volume conditions.

Constant Pressure Process

A process occurring at constant pressure imposes specific conditions on the thermodynamic system. In such processes, the heat added not only changes the internal energy of the system but also does work by changing the volume. The relationship between the work done, internal energy change, and heat added is governed by the first law of thermodynamics.

Specific Heat Capacities

This concept relates to the amount of heat required to raise the temperature of a unit mass of a substance by one degree. For gases, the specific heat capacities at constant pressure (cp) and constant volume (cv) are used to describe heat exchange in different thermodynamic processes.

Ratio of Specific Heats (?)

The ratio of specific heats, represented as ? (gamma), is defined as cp/cv for a gas. It plays a crucial role in determining the thermodynamic properties and processes involving ideal gases, particularly in adiabatic and isentropic processes.

Internal Energy Change in Ideal Gases

For an ideal gas, the change in internal energy is solely a function of temperature change, and is calculated using the specific heat at constant volume (cv). This means that regardless of the process path, any change in internal energy is determined by the temperature difference multiplied by cv and the number of moles.

Transcript

Please give Ace some feedback