First law of thermodynamics

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Question

1 mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{x R}{8}$ .The value of x is _____ [R=universal gas constant]

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Solution

$F o r D i a t o m i c g a s, γ = \frac{7}{5}$
$\begin{array}{l} △ U = Q - W = Q - \frac{Q}{5} = \frac{4 Q}{5} \\ \Rightarrow Δ U = \frac{4 Q}{5} \end{array}$
$\begin{array}{l} Also, △ U = n C_{V} Δ T \\ \Rightarrow \frac{4 Q}{5} = 1 \times \frac{5 R}{2} Δ T \\ \Rightarrow \frac{4}{5} \times 1 \times C \times Δ T = 1 \times \frac{5 R}{2} Δ T (∵ Δ Q = n C_{p} Δ T) \\ \Rightarrow C = \frac{25 R}{8} \end{array}$
$C o m p a r i n g w i t h \frac{x R}{8} w e g e t$
$S o, x = 25$

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First law of thermodynamics

Remember concepts with our Masterclasses.

1 mole of rigid diatomic gas performs a work of Q5 when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is xR8 .The value of x is _____ [R=universal gas constant]

For Diatomic gas, γ=75△U=Q−W=Q−Q5=4Q5⇒ΔU=4Q5 Also, △U=nCVΔT⇒4Q5=1×5R2ΔT⇒45×1×C×ΔT=1×5R2ΔT∵ΔQ=nCpΔT⇒C=25R8Comparing with xR8we getSo, x=25

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1 mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{x R}{8}$ .The value of x is _____ [R=universal gas constant]