Two moles of an ideal monoatomic gas at 27^∘ C occupies a volume of V. If the gas is expanded ad

step 1 In this question we have given that 2 moles of an ideal monoatomic gas at 27 degrees Celsius occ

Two moles of an ideal monoatomic gas at 27^∘ C occupies a...

Two moles of an ideal monoatomic gas at $27^{\circ} \mathrm{C}$ occupies a volume of $V$. If the gas is expanded adiabatically to the volume $2 V$, then the work done by the gas will be $\left(\gamma=\frac{5}{3}, R=8.31 \mathrm{~J} / \mathrm{mol} \mathrm{K}\right)$ (a) $+2767.23 \mathrm{~J}$ (b) $2627.23 \mathrm{~J}$ (c) $2500 \mathrm{~J}$ (d) $-2500 \mathrm{~J}$

Two moles of an ideal monoatomic gas at $27^{\circ} \mathrm{C}$ occupies a volume of $V$. If the gas is expanded adiabatically to the volume $2 V$, then the work done by the gas will be $\left(\gamma=\frac{5}{3}, R=8.31 \mathrm{~J} / \mathrm{mol} \mathrm{K}\right)$
(a) $+2767.23 \mathrm{~J}$
(b) $2627.23 \mathrm{~J}$
(c) $2500 \mathrm{~J}$
(d) $-2500 \mathrm{~J}$

Key Concepts

Adiabatic Process

An adiabatic process is one in which no heat is transferred into or out of the system. For ideal gases undergoing an adiabatic process, this means that any work done by or on the system is reflected solely in a change in the internal energy, making the process governed by the interplay between pressure, volume, and temperature without external heat exchange.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relation that describes the state of an ideal gas in terms of its pressure (P), volume (V), temperature (T), and the number of moles (n) using the gas constant (R). This law is essential for determining the initial conditions and changes in state during various thermodynamic processes, including adiabatic expansions.

First Law of Thermodynamics

The first law of thermodynamics, which states that the change in internal energy of a system equals the heat added to the system minus the work done by it, is crucial in analyzing adiabatic processes. With no heat exchange (Q = 0) in an adiabatic process, the work done by or on the system is directly equal to the change in its internal energy.

Heat Capacity Ratio

The heat capacity ratio, denoted by ? (gamma), is the ratio of the molar heat capacities at constant pressure and volume (Cp/Cv). This ratio plays a key role in adiabatic processes by determining how the pressure, volume, and temperature of the gas change during the process, especially in processes where the relationship TV^(?-1) remains constant.

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