---
title: "A sample of an ideal gas expands from an initial state \\((P_0, V_0)\\) to a final volume \\(2V_0\\) via two different thermodynamic paths, as shown in the \\(P\\text{-}V\\) diagram. In Process 1, the gas expands isothermally at temperature \\(T_0\\). In Process 2, the gas expands adiabatically from the same initial state. Which of the following correctly compares the magnitude of the work done by the gas during Process 1 (\\(W_1\\)) to the work done by the gas during Process 2 (\\(W_2\\)), and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/117450/"
date_modified: "2026-08-04T06:52:12+00:00"
---

# A sample of an ideal gas expands from an initial state \((P_0, V_0)\) to a final volume \(2V_0\) via two different thermodynamic paths, as shown in the \(P\text{-}V\) diagram. In Process 1, the gas expands isothermally at temperature \(T_0\). In Process 2, the gas expands adiabatically from the same initial state. Which of the following correctly compares the magnitude of the work done by the gas during Process 1 (\(W_1\)) to the work done by the gas during Process 2 (\(W_2\)), and provides the correct physical justification?

A sample of an ideal gas expands from an initial state \((P_0, V_0)\) to a final volume \(2V_0\) via two different thermodynamic paths, as shown in the \(P\text{-}V\) diagram. In Process 1, the gas expands isothermally at temperature \(T_0\). In Process 2, the gas expands adiabatically from the same initial state. Which of the following correctly compares the magnitude of the work done by the gas during Process 1 (\(W_1\)) to the work done by the gas during Process 2 (\(W_2\)), and provides the correct physical justification?

![A P-V diagram with vertical axis labeled P and horizontal axis labeled V. The origin is at the lower-left. A single point is marked in the upper-left region labeled (V_0, P_0). Two downward-curving paths extend from (V_0, P_0) to the right, ending at horizontal position 2V_0. The upper path is labeled Process 1 (Isothermal) and ends at pressure P_1. The lower path is labeled Process 2 (Adiabatic) and curves downward more steeply, ending at a lower pressure P_2. Ticks on the horizontal axis mark V_0 and 2V_0. Ticks on the vertical axis mark P_0, P_1, and P_2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826331-aSyedh.jpg)

- **A.** \(W_1 < W_2\), because thermal energy is continuously added to the gas during Process 1, which reduces the amount of mechanical work the gas performs compared to an insulated system.
- **B.** \(W_1 < W_2\), because all internal energy lost by the gas during Process 2 is converted directly into work without any energy lost to the environment as heat.
- **C.** \(W_1 > W_2\), because the gas in Process 1 undergoes a greater change in internal energy than in Process 2, providing more total energy to perform work.
- **D.** \(W_1 > W_2\), because as the gas expands adiabatically without heat input, its temperature and pressure drop below those of the isothermal path at every intermediate volume, resulting in a smaller area under the curve.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117450/*