Nitrogen of mass $$15$$ g is enclosed in a vessel at temperature $$300$$ K so that it does not lose any energy to external system. The amount of heat required to double the root mean square velocity of these molecules is N times $$2000$$ J. Find N. (Round$$ off answer to nearest multiple of $$10).

Question

Nitrogen of mass $$15$$ g is enclosed in a vessel at temperature $$300$$ K so that it does  not lose any energy to external system. The amount of heat required to double  the root mean square velocity of these molecules is N times $$2000$$ J. Find N.   (Round$$ off answer to nearest multiple of $$10).

Infinity Learn · Accepted Answer

Using Law of equipartition of energy,Energy of a gas at temperature T is $$U=fnRT2$$.Since, Nitrogen is diatomic, f $$=$$ $$5$$. Here, $$n=1528$$ Also,  $$vRMS=3kTm$$αTIf vRMS doubles, ⇒ T becomes $$4$$ times.So,  $$U1=55288.33002U2=55288.312002$$ So,  Δ$$U=U2$$−$$U1=515288.31200$$−$$3002=10004.5J$$≈$$10000J=5$$×$$2000J$$

Internal energy

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Nitrogen of mass 15 g is enclosed in a vessel at temperature 300 K so that it does not lose any energy to external system. The amount of heat required to double the root mean square velocity of these molecules is N times 2000 J. Find N. (Round off answer to nearest multiple of 10).

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Internal energy

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Nitrogen of mass 15 g is enclosed in a vessel at temperature 300 K so that it does not lose any energy to external system. The amount of heat required to double the root mean square velocity of these molecules is N times 2000 J. Find N. (Round off answer to nearest multiple of 10).

Using Law of equipartition of energy,Energy of a gas at temperature T is U=fnRT2.Since, Nitrogen is diatomic, f = 5. Here, n=1528 Also, vRMS=3kTmαTIf vRMS doubles, ⇒ T becomes 4 times.So, U1=55288.33002U2=55288.312002 So, ΔU=U2−U1=515288.31200−3002=10004.5J≈10000J=5×2000J

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