Question

The curves shown represent adiabatic curves for monoatomic, diatomic &polyatomic(g = 4/3) gases. The slopes for curves 1,2,3 respectively at point A are –

• A. 2.5 , 3. 5 , 4.5
• B. 2.5 $\frac { P } { T }$ , 3 $\frac { P } { T }$ , 4 $\frac { P } { T }$
• C. 2.5 $\frac { P } { T }$ , 3.5 , 4 $\frac { P } { T }$
• D. 4 $\frac { P } { T }$ , 3.5 , 2.5 $\frac { P } { T }$

Answer 1

Answer: (D)

4 $\frac { P } { T }$ , 3.5 , 2.5 $\frac { P } { T }$

Answer 2

For adiabatic process :

Slope : $\frac { \mathrm { dP } } { \mathrm { dT } }$ = $\left( \frac { \gamma } { \gamma - 1 } \right)$ $\frac { P } { T }$

g = $\frac { 5 } { 3 } \left\lvert \, \frac { \mathrm { dP } } { \mathrm { dT } } \right.$ = $\left( \frac { 5 / 3 } { 5 / 3 - 1 } \right)$ $\frac { 5 / 3 } { 2 / 3 }$

= 2.5

g = $\left( \frac { 7 / 5 } { 2 / 5 } \right)$ = 3.5

g = $\left( \frac { 4 / 3 } { 1 / 3 } \right)$ = 4