Answered: As a 3.00-mol sample of a monatomic…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

As a 3.00-mol sample of a monatomic ideal gas expands adiabatically, the work done on it is −2.50 10³ J. The initial temperature and pressure of the gas are 400 K and 2.60 atm. Calculate the following.

(a) the final temperature
K

(b) the final pressure
atm

Expert Solution

Step 1

Given:

Number of moles(n) = 3

Initial temperature(T_i) = 400 K

Initial pressure(P_i) = 2.6 atm

$W o r k d o n e (w) = - 2.5 \times 10^{3} J$

(a).

work done in adiabatic process

$\Rightarrow w = n c_{v} R (T_{f} - T_{i})$

Here, c_v for monoatomic is $\frac{3}{2}; a n d R = 8.314 J / m o l . k$

$\Rightarrow - 2.5 \times 10^{3} = 3 \times \frac{3}{2} \times 8.314 (T_{f} - 400)$

$\Rightarrow T_{f} = - \frac{5 \times 10^{3}}{9 \times 8.314} + 400$

$\Rightarrow T_{f} = 333.18 K$

Therefore the final temperature is 333.18 K

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