Q is the amount of heat added to a monoatomic ideal gas in a process in which the gas performs a work equal to Q -2 on the surrounding- The molar heat capacity for the process isA- RB- 2 RC- 3 RD- 4 R

The correct option is C 3RFrom first law of thermodynamics Δ Q=Δ U+Δ W ....(i) Here, Δ Q=Q, Δ W = Q/2 So, Δ U=Q Q/2 Δ U = Δ W =nC_v Δ T From equation (i) ...

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Standard XII

Physics

The Circular Motion

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Q is the amount of heat added to a monoatomic ideal gas in a process in which the gas performs a work equal to $\frac{Q}{2}$ on the surrounding. The molar heat capacity for the process is

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Solution

The correct option is C 3R
From first law of thermodynamics
$Δ Q = Δ U + Δ W$ ....(i)
Here, $Δ Q = Q, Δ W = \frac{Q}{2}$
So, $Δ U = Q - \frac{Q}{2}$
$Δ U = Δ W = n C_{v} Δ T$
From equation (i)
$Δ Q = 2 n C_{v} Δ T$
$n C Δ T = 2 n C_{v} Δ T$
$∴ C = 2 C_{v} = 2 \times \frac{f}{2} R = 3 R$
( $∴$ f = 3 for monoatomic gas)

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Q is the amount of heat added to a monoatomic ideal gas in a process in which the gas performs a work equal to Q2 on the surrounding. The molar heat capacity for the process is

The correct option is C 3RFrom first law of thermodynamics ΔQ=ΔU+ΔW ....(i) Here, ΔQ=Q,ΔW=Q2 So, ΔU=Q−Q2 ΔU=ΔW=nCvΔT From equation (i) ΔQ=2nCvΔT nCΔT=2nCvΔT ∴C=2Cv=2×f2R=3R (∴ f = 3 for monoatomic gas)

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