Two moles of an ideal gas at a temperature of T=273 K was isothermally expanded 4 times the ini

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Two moles of an ideal gas at a temperature of T=273 K was...

Two moles of an ideal gas at a temperature of $T=273 \mathrm{~K}$ was isothermally expanded 4 times the initial volume and then heated isochorically, so that the final pressure becomes equal to the initial pressure. The ratio of molar specific heat capacities if total amount of heat imparted to the gas equals $Q=27.7 \mathrm{~kJ}$, is : (a) $1.63$ (b) $1.66$ (c) $2.63$ (d) $1.49$

Key Concepts

Molar Specific Heat Capacities

Molar specific heat capacities refer to the amount of heat required to raise the temperature of one mole of a substance by one degree, measured either at constant pressure (cp) or constant volume (cv). The ratio of these, often represented as ? = cp/cv, is vital in determining the thermodynamic properties and behaviors of gases during different processes.

Isochoric Process

An isochoric (constant volume) process is characterized by no change in volume. In such processes, no work is done by or on the system because work in thermodynamics is associated with changes in volume. Consequently, any heat added results directly in an increase in the system’s internal energy.

First Law of Thermodynamics

The first law of thermodynamics states that the change in a system's internal energy is equal to the heat added to the system minus the work done by the system. This principle of energy conservation connects the heat transferred in various processes to changes in internal energy and work, making it crucial for analyzing composite processes involving ideal gases.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. It serves as a fundamental principle for analyzing the behavior of gases under various conditions and is particularly useful in understanding processes like isothermal and isochoric transformations.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant. For an ideal gas, this implies that any heat added to the system is used entirely to perform work since the internal energy, which depends solely on temperature for an ideal gas, does not change.

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