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Question

Find the final temperature of one mole of an ideal gas that has an initial temperature tK. The gas does 9R joules of work adiabatically. The ratio of specific heats of this gas at constant pressure and at constant volume is 43.


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Solution

Step 1: Given from the question

Given, Tinitial=tK

Work, W=9R

Ratio of specific heats

γ=CpCv=43

Step 2: Calculate the Final Temperature

In an adiabatic process, work done is given as,

W=RTfinal-Tinitial1-γ

9R=RTfinal-t1-43

91-43=Tfinal-t

Tfinal=t-93

=t-3

Hence, the required final temperature is t-3.


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