A mixture of `n_(1)` moles of monoatomic gas and `n_(2)` moles of diatomic gas has `(C_(p))/(C_(V))=gamma=1.5`
A. `n_(1) = n_(2)`
B. `2n_(1) = n_(2)`
C. `n_(1) = 2n_(2)`
D. `2n_(1) = 3n_(2)`
1 Answers
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Mixture of 10 moles of `Fe_(2)S_(3), 20` moles of `H_(2)O` and 30 moles of `O_(2)` react with `5%` yield in the given reaction : `Fe_(2)S_(3) + H_(2)O
Correct Answer - B `{:(Fe_(2)S_(3),+,3H_(2)O,+(3)/(2)O_(2),overset(50%)(rarr),2Fe(OH)_(3),+,3S,),(10 " mole ",,20 " mole",,30 " moles",,,,):}`H_(2)O` is the limiting reagent. moles of `Fe(OH)_(3) = (2)/(3) xx 20 xx 0.5 = (20)/(3)` moles
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The energy of gamma `(gamma)` ray photon is `E_(gamma)` and that of an X-rays photon is `E_(X)`. If the visible light photon has an energy of `E_(v)`,
Correct Answer - C `E_(gamma) ge 100 keV, E_(X) = 100 eV` to `100 keV`. So, we can say that `E_(y) gt E_(x) gt E_(v)`,
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Using peoperties of determinants in questions 11 to 15, prove that : `|{:(alpha,alpha^(2),beta+gamma),(beta,beta^(2),gamma+alpha),(gamma,gamma^(2),alp
L.H.S.=`|{:(alpha,alpha^(2),beta+gamma),(beta,beta^(2),gamma+alpha),(gamma,gamma^(2),alpha+beta):}|=|{:(alpha,alpha^(2),alpha+beta+gamma),(beta,beta^(2),alpha+beta+gamma),(gamma,gamma^(2),alpha+beta+gamma):}|` `(C_(3)toC_(3)+C_(1))` `=(alpha+beta+gamma)|{:(alpha,alpha^(2),1),(beta,beta^(2),1),(gamma,gamma^(2),1):}|` `(alpha+beta+gamma)|{:(alpha,alpha^(2),1),(beta-alpha,beta^(2)-alpha^(2),0),(gamma-alpha,gamma^(2)-alpha^(2),0):}|` `(R_(2)toR_(2)-R_(1),R_(3)toR_(3)-R_(1))` `(alpha+beta+gamma)(beta-alpha)(gamma-alpha)|{:(alpha,alpha^(2),1),(1,beta-alpha,0),(1,gamma-alpha,0):}|` `=-(alpha-beta)(gamma-alpha)(alpha+beta+gamma)1.|{:(1,beta+alpha),(1,gamma+alpha)` `=-(alpha-beta)(gamma-alpha)(alpha+beta+gamma)(gamma+alpha-beta-alpha)` `=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)` =R.H.S.
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`5`n , n and `5`n moles of a monoatomic , diatomic and non-linear polyatomic gases (which do not react chemically with each other ) are mixed at room
Correct Answer - D `f_(eq) = (f_(1)n_(1) + f_(2)n_(2) + f_(3)n_(3))/(n_(1) + n_(2)+ n_(3)) = ((5n) (3)(n)(5)+(5n)(6))/(5n + n+ 5n) = (50)/(11)`
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Four moles of hydrogen , two moles of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant press
Correct Answer - A `C_("pmix") = (n_(1)Cp_(1)+ n_(2)Cp_(2) + n_(3)Cp_(3))/(n_(1) + n_(2) + n_(3))` =`((4) ((7)/(2)R) + 2 ((5)/(2)R) + 1 (4R))/( 4+ 2 + 1 ) = (23)/(7)R`
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Molar heat capacity of an ideal gas in the process `PV^(x)` = constant , is given by : `C = (R)/(gamma-1) + (R)/(1-x)`. An ideal diatomic gas with `C_
Correct Answer - A `P alpha V implies PV^(-1) = "constant" implies x = -1` `implies C = C_(V) +(R)/(2) = (5R)/(2) + (R)/(2) = 3R`
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One mole of ideal monoatomic gas `(gamma=5//3)` is mixed with one mole of diatomic gas `(gamma=7//5)`. What is `gamma` for the mixture? `gamma` Denote
Correct Answer - B Monoatomic `" "` `n_(1) = 1` Diatomic `n_(2) = 1 gamma_(2) = (7)/(5)` `(n_(1) + n_(2))/(gamma_("mix") - 1) = (n_(1))/(gamma_(1) - 1) + (n_(2))/(gamma_(2) - 1) implies...
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One mole of an ideal monoatomic gas `(gamma = (5)/(3))` is mixed with one mole of a diatomic gas `(gamma=(7)/(5))`. (`gamma` denotes the ratio of spec
`gamma_(mix)=(C_(P_("mix")))/(C_(V_("mix")))=(1+(5)/(2)R+1xx(7)/(2)R)/(1xx(3)/(2)+1xx(5)/(2)R)`
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When a mixture of 10 moles of `SO_(2)` and 16 moles of `O_(2)` were passed over a catalyst, 8 moles of `SO_(3)` were formed at equilibrium. The number
Correct Answer - A `2SO_(2)(g)+O_(2)(g) Leftrightarrow 2SO_(3)(g)` `{:(,t=0,10,16,0),(,t_(eq),(10-2x),(16-x),0),(, ,(2x=8), ,x=4):}` `therefore "Remaining "SO_(2)=10-8=2"mol"` ` "Remaining "O_(2)=16-4=12"mol"`
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If `alpha, beta, gamma` are three real numbers and `A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),
Correct Answer - A::B::D `A=[(cos alpha,sin alpha,0),(cos beta,sin beta,0),(cos gamma,sin gamma,0)][(cos alpha,cos beta,cos gamma),(sin alpha,sin beta,sin gamma),(0,0,0)]` Clearly, A is symmetric and `|A|=0`, hence, singular and not invertiable. Also, `A A^(T)...
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