An ideal gas with heat capacity at constant volume Cv undergoes a quasistatic process described by pVα in a p-V diagram, where a is a constant. The heat capacity of the gas during this process is given by

Question

An ideal gas with heat capacity at constant volume Cv undergoes a quasistatic process described by pVα in a p-V diagram, where a is a constant. The heat capacity of the gas during this process is given by (A) CV (B) CV+nR (C) CV+(nR/1-α) (D) CV+(nR/1-α2)

Tardigrade Admin · Accepted Answer

Process equation is pVα=constant (k) ⇒ p=(k/Vα) Work done by the gas in given process is Δ W∫ViVfpdV =∫ViVf (kdV/Vα)=[(kV1-α/1-α)] Vf =[(pV/1-α)]ViVf=(p(Vf-Vi)/1-α) =(pΔ V/1-α)=(nRΔ T/1-α) The change of internal energy of gas inthis process will be Δ U=CVΔ T And if Δ Q is heat supplied to the gasthen, Δ Q=cΔ T Now, by first law of thermodynamics, wehave Δ Q=Δ U+Δ W ⇒ CΔ T=CVΔ T+(nRΔ T/1-α) Heat capacity of the gas is ⇒ C=CV+(nR/1-α)

Q. An ideal gas with heat capacity at constant volume $C_{v}$ undergoes a quasistatic process described by $p V^{α}$ in a $p - V$ diagram, where a is a constant. The heat capacity of the gas during this process is given by

$C_{V}$

$C_{V} + n R$

$C_{V} + \frac{n R}{1 - α}$

$C_{V} + \frac{n R}{1 - α ^{2}}$

Q. An ideal gas with heat capacity at constant volume Cv​ undergoes a quasistatic process described by pVα in a p−V diagram, where a is a constant. The heat capacity of the gas during this process is given by

CV​

CV​+nR

CV​+1−αnR​

CV​+1−α2nR​

Q. An ideal gas with heat capacity at constant volume $C_{v}$ undergoes a quasistatic process described by $p V^{α}$ in a $p - V$ diagram, where a is a constant. The heat capacity of the gas during this process is given by

$C_{V}$

$C_{V} + n R$

$C_{V} + \frac{n R}{1 - α}$

$C_{V} + \frac{n R}{1 - α ^{2}}$