Question

A diatomic ideal gas undergoes expansion through different processes shown in the column-I. Answer the following questions based on these columns.
$\begin{array}{cccccc}& ColumnI& & Column2& & Column3\\ \left(I\right)& P^2\propto \frac{1}{V^3}& \left(i\right)& \Delta T>0& \left(P\right)& \Delta Q>0\\ \left(II\right)& T^5\propto \frac{1}{V}& \left(ii\right)& \Delta T<0& \left(Q\right)& \Delta Q=0\\ \left(III\right)& P^5\propto \frac{1}{V^7}& \left(iii\right)& \Delta T=0& \left(R\right)& \Delta Q<0\\ \left(IV\right)& P^5\propto \frac{1}{V^4}& \left(iv\right)& Ca{n}^{\prime }tsay& \left(S\right)& Ca{n}^{\prime }tsay\end{array}$
Which of the combination is correct for process (IV) i.e.
$(P^5\propto \frac{1}{V^4})$?

• A. (IV) (i) (P)
• B. (IV) (ii) (R)
• C. (IV) (iii) (S)
• D. (IV) (ii) (P)

Answer 1

The correct option is A (IV) (i) (P)

$\Delta Q=nC\Delta T$
$C=C_V+\frac{R}{1-x}$ (for the process $P{V}^x$ = constant)
and $C_v=\frac{5}{2}R$ (for diatmic gas)
As gas is under expansion so PV = nRT can be used for the various process shown to get the temperature variation ($\Delta$T) and hence $\Delta$ Q can be found using above equation.