One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is (α2/4) R J / mol K; then the value of α will be . (Assume that the given diatomic gas

Question

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is (α2/4) R J / mol K; then the value of α will be . (Assume that the given diatomic gas (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

C v / mix =( n 1 Cv 1+ n 2 Cv 2/ n 1+ n 2) =(1 ⋅ (3 R /2)+3 ⋅ (5 R /2)/1+3) =(9 R /4)=(α2/4) R α=3

Q. One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{α ^{2}}{4} R J / m o l K$ ; then the value of $α$ will be ____. (Assume that the given diatomic gas

$C_{v} / mi x = \frac{n _{1} C v _{1} + n _{2} C v _{2}}{n _{1} + n _{2}}$
$= \frac{1 \cdot \frac{3 R}{2} + 3 \cdot \frac{5 R}{2}}{1 + 3}$
$= \frac{9 R}{4} = \frac{α ^{2}}{4} R$
$α = 3$

Q. One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is 4α2​RJ/molK; then the value of α will be ____. (Assume that the given diatomic gas

Cv​/mix=n1​+n2​n1​Cv1​+n2​Cv2​​ =1+31⋅23R​+3⋅25R​​ =49R​=4α2​R α=3

Q. One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{α ^{2}}{4} R J / m o l K$ ; then the value of $α$ will be ____. (Assume that the given diatomic gas

$C_{v} / mi x = \frac{n _{1} C v _{1} + n _{2} C v _{2}}{n _{1} + n _{2}}$
$= \frac{1 \cdot \frac{3 R}{2} + 3 \cdot \frac{5 R}{2}}{1 + 3}$
$= \frac{9 R}{4} = \frac{α ^{2}}{4} R$
$α = 3$