Answered: 20-2 An ideal gas undergoes the…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

An ideal gas undergoes the thermodynamic process shown in the PV
diagram in the figure. Determine whether each of the values (a) ∆U,
(b)W , (c)Q for the gas is positive, negative, or zero. (Note that W is
the work done on the gas.) Hint: First use the ideal gas law to find the
initial and final temperatures in terms of P0 and V0 and determine if
the final temperature is greater than, less than, or equal to the initial
temperature.
∆U ?
W?

**Thermodynamic Process of an Ideal Gas**

**Problem 20-2:**

An ideal gas undergoes the thermodynamic process shown in the PV diagram.

**Objective:**

Determine whether each of the following values is positive, negative, or zero:
- (a) Change in internal energy (ΔU)
- (b) Work done on the gas (W)
- (c) Heat added to the system (Q)

**Notes:**
- W represents the work done on the gas.
- Use the ideal gas law to find the initial and final temperatures in terms of \( P_0 \) and \( V_0 \).
- Determine if the final temperature is greater than, less than, or equal to the initial temperature.

**PV Diagram Explanation:**

The diagram illustrates a thermodynamic process in the Pressure-Volume plane:
- The initial state is at pressure \( P_0 \) and volume \( V_0 \).
- The final state is at pressure \( 2P_0 \) and volume \( 2V_0 \).
- The process follows a path where pressure first increases at constant volume (vertical line), and then volume increases at constant pressure (horizontal line).

**Questions:**

- ΔU?
- W?
- Q?

**Hint for Solution:**

Apply the ideal gas law, \( PV = nRT \), to find the changes in temperature, and analyze how these affect ΔU, W, and Q according to the first law of thermodynamics: \(\Delta U = Q - W\).

Consider the geometric area under the PV curve for calculating work and relate it to energy changes in the system.

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