Thermodynamic processes

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Question

The value of $γ = C_{P} / C_{V}$ is 4/3 for an adiabatic process of an ideal gas for which internal energy $U = K + nPV$ . The value of n (K is a constant) is ____.

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Solution

${PV}^{γ} = constant$
${PV}^{4 / 3} = constant$
$In (V^{4}) + In (P^{3}) = constant$
$4 (\frac{dV}{V}) = - 3 (\frac{dP}{P})$
$4 P (dV) + 3 V (dP) = 0$
$3 (PdV + VdP) + PdV = 0$ …(i)
For adiabatic process, $dQ = 0 = dU + dW$
$= dU + PdV$ …(ii)
Compare Eqs. (i) and (ii), $dU = 3 (PdV + VdP)$
$U = K + 3 PV$
So, n = 3

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Thermodynamic processes

Remember concepts with our Masterclasses.

The value of γ=CP/CV is 4/3 for an adiabatic process of an ideal gas for which internal energy U=K+nPV. The value of n (K is a constant) is ____.

PVγ= constant PV4/3= constant In V4+In P3= constant 4dVV=−3dPP4P(dV)+3V(dP)=03(PdV+VdP)+PdV=0 …(i)For adiabatic process, dQ=0=dU+dW=dU+PdV …(ii)Compare Eqs. (i) and (ii), dU=3(PdV+VdP)U=K+3PVSo, n = 3

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The value of $γ = C_{P} / C_{V}$ is 4/3 for an adiabatic process of an ideal gas for which internal energy $U = K + nPV$ . The value of n (K is a constant) is ____.