N1 and n2 moles of two ideal gases of thermodynamics constant - 1 and - 2 respectively are mixed- for the mixture is -

N=n_1+n_2 W=U_1+U_2 nC_V=n_1C_V1+n_2C_V2 =n_1R/γ_1 1+n_2R/γ_2 1 C_P=nC_V nC_P=n_1γ_1R/γ_1 1+n_2γ_2R/γ_2 1 γ=nC_P/nC_V=C_P/C_V n_1γ_1 R/γ_1 1+n_2γ_2R/γ_2 1/ ...

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Byju's Answer

Standard XI

Physics

Heat Capacity

n1 and n2 mol...

Question

$n_{1}$ and $n_{2}$ moles of two ideal gases of thermodynamics constant $γ_{1}$ and $γ_{2}$ respectively are mixed, for the mixture is –

\frac{γ_{1} + γ_{2}}{2}

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\frac{n_{1} γ_{1} + n_{2} γ_{2}}{n_{1} + n_{2}}

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\frac{n_{1} γ_{2} + n_{2} γ_{1}}{n_{1} + n_{2}}

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= \frac{n_{1} γ_{1} (γ_{2} - 1) + n_{2} γ_{2} (γ_{1} - 1)}{n_{1} (γ_{2} - 1) + n_{2} (γ_{1} - 1)}

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Solution

The correct option is D $= \frac{n_{1} γ_{1} (γ_{2} - 1) + n_{2} γ_{2} (γ_{1} - 1)}{n_{1} (γ_{2} - 1) + n_{2} (γ_{1} - 1)}$
$n = n_{1} + n_{2} W = U_{1} + U_{2} n C_{V} = n_{1} C_{V 1} + n_{2} C_{V 2} = n_{1} \frac{R}{γ_{1} - 1} + n_{2} \frac{R}{γ_{2} - 1} C_{P} = n C_{V} n C_{P} = n_{1} γ_{1} \frac{R}{γ_{1} - 1} + n_{2} γ_{2} \frac{R}{γ_{2} - 1} γ = \frac{n C_{P}}{n C_{V}} = \frac{C_{P}}{C_{V}}$
$\frac{\frac{n_{1} γ_{1} R}{γ_{1} - 1} + n_{2} γ_{2} \frac{R}{γ_{2} - 1}}{\frac{R}{n_{1} (γ_{2} - 1)} + n_{2} \frac{R}{(γ_{1} - 1)}}$
$= \frac{n_{1} γ_{1} (γ_{2} - 1) + n_{2} γ_{2} (γ_{1} - 1)}{n_{1} (γ_{2} - 1) + n_{2} (γ_{1} - 1)}$

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n1 and n2 moles of two ideal gases of thermodynamics constant γ1 and γ2 respectively are mixed, for the mixture is –

The correct option is D =n1γ1(γ2−1)+n2γ2(γ1−1)n1(γ2−1)+n2(γ1−1)n=n1+n2W=U1+U2nCV=n1CV1+n2CV2=n1Rγ1−1+n2Rγ2−1CP=nCVnCP=n1γ1Rγ1−1+n2γ2Rγ2−1γ=nCPnCV=CPCV n1γ1Rγ1−1+n2γ2Rγ2−1Rn1(γ2−1)+n2R(γ1−1) =n1γ1(γ2−1)+n2γ2(γ1−1)n1(γ2−1)+n2(γ1−1)

$n_{1}$ and $n_{2}$ moles of two ideal gases of thermodynamics constant $γ_{1}$ and $γ_{2}$ respectively are mixed, for the mixture is –