Heat and Thermodynamics 5 Question 27
28. An ideal monoatomic gas is taken round the cycle $A B C D A$ as shown in the $p-V$ diagram (see figure). The work done during the cycle is
(1983, 1M)
(a) $p V$
(b) $2 p V$
(c) $\frac{1}{2} p V$
(d) zero
Match the Columns
Directions (Q.Nos. 15-18) Matching the information given in the three columns of the following table.
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $p-V$ diagrams in column 3 of the table. Consider only the path from state 1 to state 2 . $W$ denotes the corresponding work done on the system. The equations and plots in the table have standards notations and used in thermodynamic processes. Here $\gamma$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is $n$.
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Solution:
- Work done in a cyclic process $=$ area between the cycle
$$ =A B \times B C=(2 p-p) \times(2 V-V)=p V $$
NOTE If cycle is clockwise ( $p$ on $Y$-axis and $V$ on $X$-axis) work done is positive and if it is anti-clockwise work done is negative.
