The ideal gas equation for real gases:

$\overline{){\mathbf{P}}{\mathbf{V}}{\mathbf{=}}{\mathbf{n}}{\mathbf{R}}{\mathbf{T}}}$, where P is the gas pressure, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the absolute gas temperature.

Change in the gas internal energy:

$\overline{){\mathbf{\u2206}}{{\mathbf{E}}}_{\mathbf{t}\mathbf{h}}{\mathbf{=}}\frac{\mathbf{3}}{\mathbf{2}}{\mathbf{n}}{\mathbf{R}}{\mathbf{\u2206}}{\mathbf{T}}}$

Work done by the gas:

$\overline{){{\mathbf{W}}}_{\mathbf{g}\mathbf{a}\mathbf{s}}{\mathbf{=}}{\mathbf{P}}{\mathbf{\u2206}}{\mathbf{V}}}$, where ΔV= V_{2} - V_{1}.

The temperature of the monoatomic gas at the different points can be found from the ideal gas equation:

__At Point 1:__

T_{1} = P_{1}V_{1}/nR

From the graph, we substitute as follows:

T_{1} = (4)(101.3 × 10^{3})(800 × 10^{-6})/(0.1)(8.31) = 390.1 K

0.10 mol of a monatomic gas follows a process shown in the figure.

1. How much energy is transferred to or from the gas during process 2 to 3?

2. What is the total change in thermal energy of the gas?

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