Ten moles of an ideal gas at constant temperature 600 K is compressed from 100 L to 10 L. The

step 1 In this question we have given that 10 moles of an ideal gas at constant temperature is compress

Ten moles of an ideal gas at constant temperature 600 K is...

Ten moles of an ideal gas at constant temperature $600 \mathrm{~K}$ is compressed from $100 \mathrm{~L}$ to $10 \mathrm{~L}$. The work done in the process is (a) $4.11 \times 10^{4} \mathrm{~J}$ (b) $-4.11 \times 10^{4} \mathrm{~J}$ (c) $11.4 \times 10^{4} \mathrm{~J}$ (d) $-11.4 \times 10^{4} \mathrm{~J}$

Ten moles of an ideal gas at constant temperature $600 \mathrm{~K}$ is compressed from $100 \mathrm{~L}$ to $10 \mathrm{~L}$. The work done in the process is
(a) $4.11 \times 10^{4} \mathrm{~J}$
(b) $-4.11 \times 10^{4} \mathrm{~J}$
(c) $11.4 \times 10^{4} \mathrm{~J}$
(d) $-11.4 \times 10^{4} \mathrm{~J}$

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Key Concepts

Ideal Gas

An ideal gas is a theoretical construct where the gas particles do not interact except through elastic collisions and the gas follows the ideal gas law, PV = nRT. This concept is foundational in thermodynamics for analyzing the behavior of gases under different conditions without accounting for intermolecular forces.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant. In the context of an ideal gas, the constancy of temperature implies that the product nRT remains unchanged, and any compression or expansion of the gas leads to adjustments in pressure and volume according to the ideal gas law.

Work in a Reversible Isothermal Process

When an ideal gas undergoes a reversible isothermal process, the work done by or on the gas can be calculated by integrating the pressure with respect to volume. This results in the expression W = -nRT ln(V_f/V_i), where the negative sign conventionally indicates work done on the system during compression.

Natural Logarithm

The natural logarithm (ln) is essential in calculating the work done during a reversible isothermal process because it arises from the integral of 1/V with respect to V. This mathematical function captures the relationship between the initial and final volumes of the gas during expansion or compression.

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