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  • Two mole of hydrogen and  mole of Helium are mixed at room temperature and at atmospheric pressure <img alt="\mathrm

Two mole of hydrogen and 3 mole of Helium are mixed at room temperature and at atmospheric pressure \mathrm{Pa} and the mixture occupies a volume V

Option: 1

C_V of mixture is 2 R.


Option: 2

C_p of mixture is 2.9 R.


Option: 3

\gamma of mixtion is nearly 1.53.


Option: 4

If the mixtwo is expanded adiabatically to 2 \mathrm{V} pressure is \frac{P a}{2^{1.4}}.


Answers (1)

best_answer

Hydrogen: 

n=2, C_V=\frac{5}{2} R ; C_p=\frac{7}{2} R
Helium:

n=3, C_V=\frac{3}{2} R ; C_P=\frac{5}{2} R
Mixtuore:

\begin{aligned} C_V & =\frac{n_1 C_{V_1}+n_2 C_{V_2}}{n_1+n_2} \\ & =\frac{\left(\frac{2 \times 5}{2} R\right)+\left(\frac{3 \times 3}{2} R\right)}{2+3}\\&=\frac{19 R}{10}\\&=1.9 R \end{aligned}
Option (a) is wrong.

C_p=C_V+R=1.9 R+R=2.9 R
Option (b) is correct.

\gamma=\frac{C_p}{n}=\frac{29}{19} \simeq 1.526 \simeq 1.53

Option(c) is comect.

\begin{aligned} P_a V^\gamma&=P^{\prime}(2 V)^\gamma\\ \Rightarrow P^{\prime}&=\frac{P_a}{2^\gamma}=\frac{P_a}{2^{1.53}}\end{aligned}
Option (d) is wrong.

Posted by

Suraj Bhandari

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