Question

An ideal gas is subjected to a thermodynamic process PV-I = 0.4 where P is pressure in pascal and Q
Vis volume in (metre). What is the slope of the P-V curve with volume plotted aganist x-axis at
V=1 m ?​

Answer 1

Given that,

An ideal gas is subjected to a thermodynamic process

$PV^{2.5}=0.4$

Volume = 1 m³

We know that,

The P-V curve is $\dfrac{dP}{dV}$.

We need to calculate the slope of the P-V curve

Using given equation

$PV^{2.5}=0.4$

$PV^{\frac{5}{2}}=\dfrac{2}{5}$

$P=V^{-\frac{5}{2}}\times\dfrac{2}{5}$

On differentiating w.r.to V

$\dfrac{dP}{dV}=\dfrac{2}{5}\times(-\dfrac{5}{2})\times V^{-\dfrac{7}{2}}$

Put the value of V

$\dfrac{dP}{dV}=\dfrac{2}{5}\times(-\dfrac{5}{2})\times(1)^{-\dfrac{7}{2}}$

$\dfrac{dP}{dV}=-1$

Hence, The slope of the P-V curve is -1.