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A certain quantity at real gas occupies a volume of \mathrm{1 \mathrm{~dm}^3} at 100 atm and 300 K when its compressibility factor is 1.07. Its volume at 300 atm and 200 K [when its compressibility factor is 1.4 ] is ----- \mathrm{10^{-4} \mathrm{dm}^3 \text { ? }} ?

Option: 1

.03985 \mathrm{dm}^3


Option: 2

.2907 d m^3


Option: 3

.2407 d m^3


Option: 4

.3925 d m^3


Answers (1)

best_answer

\mathrm{\begin{aligned} & z=\frac{P_V}{n R T} \\ & n=\frac{P_V}{2 R T} \end{aligned}}

\mathrm{\begin{aligned} & z_1=1.07, P_1=100 \mathrm{~atm} \quad v_1=1, T_1=300 \mathrm{ks} \\ & z_2=1.4, P_2=300 \mathrm{~atm} \quad v_2=?, T_2=200 \mathrm{~K} \end{aligned}}

\mathrm{\begin{aligned} & \frac{z_1}{z_2}=\frac{P_1 v_1 T_2}{P_2 v_2 T_1}= \\ & \frac{1.07}{1.4}=\frac{100 \times 1 \times 200}{300 \times v_2 \times 300} \\ & v_2=\frac{100 \times 200 \times 1.4}{300 \times 300 \times 1.07}=\frac{28000}{96,300} \\ & v_2=.2907 \mathrm{dm}^3 \end{aligned}}

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rishi.raj

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