Question

Pressure versus density graph of an ideal gas is shown in figure. Choose the correct option.

• A. During the process AB work done by the gas is positive
• B. During the process AB work done by the gas is negative
• C. During the process BC internal energy of the gas is increasing
• D. None of the above

Answer 1

The correct option is A During the process AB work done by the gas is positive

Solution

We know that,

f(density = $\frac{nM}{V}$ [Mass = moles $\times$ Molar mass](Volume)

so, $V=\frac{nM}{f}$ ___ (i)

In process AB f = constant,

Also, V $\to$ constant [By eq - (i)]

so, $\Delta W=\Delta PU$

As $\Delta P=+ve$ [P is increasing from A to B]

$\Delta W=\Delta PV=V\Delta P+P\Delta V=V\Delta P$ to

$\Delta W=V\Delta P=+ve$

In process B-C, we have

$\frac{PM}{RT}=f\Rightarrow T=\frac{PM}{RP}$

As $\frac{P}{f}\to$ constant, $T=\left(\frac{P}{f}\right)\frac{M}{R}\to$ constant

Internal energy (nCVT) will remain

same -

Option - A is correct.