Heat and Thermodynamics 5 Question 28
29. One mole of a monoatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $p V$-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-l with the corresponding statements in List-II.
(2018 Adv.)
| List-I | List-II | ||
|---|---|---|---|
| P. | In process I | 1. | Work done by the gas is zero |
| Q. | In process II | 2. | Temperature of the gas remains unchanged |
R. In process III 3. No heat is exchanged between
S. In process IV 4. Work done by the gas is $6 p _0 V _0$
(a) $P \rightarrow 4$; $Q \rightarrow 3$; $R \rightarrow 1$; $S \rightarrow 2$
(b) $P \rightarrow 1 ; Q \rightarrow 3 ; R \rightarrow 2 ; S \rightarrow 4$
(c) $P \rightarrow 3$; $Q \rightarrow 4$; $R \rightarrow 1 ; S \rightarrow 2$
(d) $P \rightarrow 3$; $Q \rightarrow 4 ; R \rightarrow 2 ; S \rightarrow 1$
| Column 1 | Column 2 | Column 3 |
|---|
(III)
$W _{1 \rightarrow 2}=0$
(iii) Isobaric
(R)
(IV) $W _{1 \rightarrow 2}=-n R T$ $\ln \left(\frac{V _2}{V _1}\right)$ (iv) Adiabatic
(S)
Show Answer
Solution:
- $\left(\frac{d p}{d V}\right) _{\text {adiabatic }}=\gamma\left(\frac{d p}{d V}\right) _{\text {isothermal }}$
List-I
(P) Process I $\quad \Rightarrow$ Adiabatic $\Rightarrow Q=0$
(Q) Process II $\Rightarrow$ Isobaric
$\therefore \quad W=p \Delta V=3 p _0\left[3 V _0-V _0\right]=6 p _0 V _0$
(R) Process III $\Rightarrow$ Isochoric $\Rightarrow W=0$
(S) Process (IV) $\Rightarrow$ Isothermal $\Rightarrow$ Temperature $=$ Constant
