A cubical box of side $$1$$ m contains helium gas (atomic$$ weight $$4) at a pressure of $$100$$ Nm–$$2$$. During an observation time of $$1$$ second, an atom travelling with $$root-$$ $$mean-square$$ speed parallel to one of the edges of the cube was found to make $$500$$ hits with a particular wall, without any collision with other atoms. Take R $$=$$ $$253$$ J mol–$$1K$$–$$1$$ and k $$=$$ $$1.38$$×$$10$$–$$23J$$ K–$$1$$. Evaluate average kinetic energy.

Question

A cubical box of side $$1$$ m contains helium gas (atomic$$ weight $$4) at a pressure of   $$100$$ Nm–$$2$$. During an observation time of $$1$$ second, an atom travelling with $$root-$$ $$mean-square$$ speed parallel to one of the edges of the cube was found to make  $$500$$ hits with a particular wall, without any collision with other atoms. Take R $$=$$  $$253$$  J mol–$$1K$$–$$1$$  and k $$=$$ $$1.38$$×$$10$$–$$23J$$ K–$$1$$. Evaluate average kinetic energy.

Infinity Learn · Accepted Answer

Distance travelled in one second  $$=500$$×$$2m=1000m$$.  So, $$vRMS=1000$$ ms−$$1But$$  $$vRMS=3RTM$$⇒$$T=160KAverage$$ kinetic energy per atom $$=$$  $$32kT=32$$×$$1.38$$×$$10$$–$$23$$×$$160$$ $$=$$ $$3.312$$×$$10$$–$$21J$$

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