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  • If 2 mol of a gas at constant pressure, requires 70 cal heat to increase its temperature from 30 0C to 35 0C , then find its degree of freedom?<str

If 2 mol of a gas at constant pressure, requires 70 cal heat to increase its temperature from 30 0C to 35 0C , then find its degree of freedom?

Option: 1

5


Option: 2

6


Option: 3

7


Option: 4

8


Answers (1)

best_answer

Work done at constant pressure,

\begin{aligned} \Delta \omega=P \Delta V & =n R \Delta T \\ & =2 \times 2 \times 5(\because \Delta T=308-303=5 \mathrm{k}) \\ & =20 \mathrm{cal} \end{aligned}Given that, heat required,

\begin{aligned} &\Delta Q=n C_p \Delta T=70 \mathrm{cal}\\ &\therefore C_p=\frac{70}{2 \times 5}={7 \mathrm{cal} /\mathrm{mol} \mathrm{K}}{} \end{aligned}

\begin{gathered} C_V=C_P-R=7-2=5 \mathrm{cal} / \mathrm{molK} \\ \gamma=\frac{C_P}{C_V}=\frac{7}{5} \end{gathered}

Again, 

\gamma=1+\frac{2}{f} \Rightarrow \frac{7}{5}=1+\frac{2}{f} \Rightarrow \frac{2}{f}=\frac{7}{5}-1=\frac{7-5}{5}=\frac{2}{5}

\Rightarrow \frac{2}{7}=\frac{2}{5} \Rightarrow f=5

Posted by

manish painkra

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