Kinetic Theory

JEE Main level, single correct, medium

101 of 168

Question 101 of 168

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? (R=8.3J/molK)\left(R=8.3J/molK\right)

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Answer: (A) 17.4J/molK17.4J/molK

(Cv)mix=n1Cv1+n2Cv2n1+n2=2(32R)+3(52R)2+3{\left({C}_{v}\right)}_{mix}=\dfrac{{n}_{1}{C}_{{v}_{1}}+{n}_{2}{C}_{{v}_{2}}}{{n}_{1}+{n}_{2}}=\dfrac{2\left(\dfrac{3}{2}R\right)+3\left(\dfrac{5}{2}R\right)}{2+3}
=3R+152R5=2110R=17.4J/molK=\dfrac{3R+\dfrac{15}{2}R}{5}=\dfrac{21}{10}R=17.4J/molK

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