On $P-V$ coordinates, the slope of an isothermal curve of a gas at a pressure $P=1 \mathrm{MPa}$ and volume…
On $P-V$ coordinates, the slope of an isothermal curve of a gas at a pressure $P=1 \mathrm{MPa}$ and volume $V=0.0025 \mathrm{~m}^{3}$ is equal to $-400 \mathrm{MPa} / \mathrm{m}^{3}$. If $C_{p} / C_{v} =1.4$, the slope of the adiabatic curve passing through this point is :
$-56 \mathrm{MPa} / \mathrm{m}^{3}$
$-400 \mathrm{MPa} / \mathrm{m}^{3}$
$-560 \mathrm{MPa} / \mathrm{m}^{3}$
None of these
Solution
Slope of adiabatic curve $=\gamma \times$ slope of isothermal curve $=1.4 \times(-400)=-560 \mathrm{MPa} / \mathrm{m}^{3}$
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