First slide

Calculation of pressure

Question

At a pressure of 24 × 10⁵ dyne/cm², the volume of O₂ is 10 litre and mass is 20 gm. The r.m.s velocity will be

Easy

A

800 m/sec
B

400 m/sec
C

600 m/sec
D

200 m/sec

Solution

$\frac{1}{2}.m\,{V^2}_{rms}\, = \,\frac{3}{2}PV$
$P\, = \,24 \times {10^5} \times \frac{{{{10}^{ - 5}}}}{{{{10}^{ - 4}}}}N/{m^2}\, = \,24 \times {10^4}N/{m^2}$
$V\, = \,10lit\, = \,10 \times {10^{ - 3}}{m^3}$
${V_{rms}}\, = \sqrt {\frac{{3PV}}{m}} \, = \,\sqrt {\frac{{3 \times 24 \times {{10}^4} \times {{10}^{ - 2}}}}{{20 \times {{10}^{ - 3}}}}} \, = \,600m/s$

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