Answered: One mole of an ideal gas undergoes the…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

One mole of an ideal gas undergoes the cycle, A⟶B⟶C⟶A, as shown in the graph. For this gas, C_V = 1.5R. Step C⟶A is isothermal and reversible.

1) Calculate q for each step in the process.

A
1.0
B
0.5
C
22.4
44.8
Volume (L)
Pressure (atm)

Expert Solution

Step 1

$\begin{array}{rcl} F i r s t l a w o f T h e r m o d y n a m i c s; ∆ U & = & q + W \\ q & = & ∆ U - W \end{array}$

$T h e p r o c e s s A \to B i s a n i s o b a r i c p r o c e s s, c o n s \tan t p r e s s u r e (1.0 a t m) ∆ U = q + W q = n C_{v} ∆ T - P (V_{2} - V_{1}) q = n C_{v} (\frac{P . ∆ V}{n R}) - P (V_{2} - V_{1}) S u b s t i t u t i n g t h e v a l u e s, q = 1.5 R (\frac{1 \times (44.8 - 22.4)}{R}) - 1 \times (44.8 - 22.4) q = 11.2 L a t m q_{A \to B} = 11.2 L a t m \times \frac{8.314 J}{0.0821 L a t m} = 1.134 k J$

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