P-V graph for an ideal gas undergoing polytropic process $P V^{m} = c o n s t a n t$ is shown here. Find the value of m.

Open in App

Solution

Slope of the curve, $\frac{d P}{d V} = t a n (180 - 37) = t a n 143^{o} = - 0.75$
The given polytropic process $P V^{m} = c o n s t a n t$
Differentiating, we get $P \times m V^{m - 1} d V = V^{m} d P = 0$
$∴$ $m P V^{m - 1} d V = - V^{m} d P$
$⟹$ $\frac{d P}{d V} = - \frac{m P}{V}$
$∴$ $- 0.75 = - \frac{m \times 2 \times 10^{5}}{4 \times 10^{5}}$ $⟹ m = 1.5$

Suggest Corrections

Similar questions

P - V

graph for an ideal gas undergoing a polytropic process given by

P V^{n} = k

is shown below. Find the value of

n

Q. Find the molar heat capacity of an ideal gas with adiabatic exponent

^{'} γ^{'}

for the polytropic process

P V^{n} = c o n s t a n t

Q. For polytropic process

{P V}^{n} =

constant,

C_{m}

(molar heat capacity) of an ideal gas is given by:

Q. An ideal gas undergoes a polytropic given by equation

P V^{n} =

constant. If molar heat capacity of gas during this process is arithmetic mean of its molar heat capacity at constant pressure and constant volume then value of

n

is:

Figure 17.5 shows the P - V diagram for a fixed mass of an ideal gas undergoing cyclic process ABCA.AB represents isothermal process. Which of the graphs shown in Fig. 17.6 represents the P - T diagram of the cyclic process ?

Join BYJU'S Learning Program

P-V graph for an ideal gas undergoing polytropic process PVm=constant is shown here. Find the value of m.

Slope of the curve, dPdV=tan(180−37)=tan143o=−0.75The given polytropic process PVm=constantDifferentiating, we get P×mVm−1dV=VmdP=0∴ mPVm−1dV=−VmdP⟹ dPdV=−mPV∴ −0.75=−m×2×1054×105 ⟹m=1.5

P-V graph for an ideal gas undergoing polytropic process $P V^{m} = c o n s t a n t$ is shown here. Find the value of m.