Question

Which one is the correct option depicting the two different thermodynamic processes?

• A. (c) and (d)
• B. (b) and (c)
• C. (a) only
• D. (c) and (a)

Answer 1

The correct option is A

(c) and (d)

Step :1 Given information

Two thermodynamic processes are Isothermal and adiabatic.

Step:2 Formula for the two processes

1. Isothermal process: It is a thermodynamic process in which the temperature of a system remains constant.
2. Adiabatic process: It is a process in which no heat transfer takes place into or out from the system.

$P{V}^{\gamma }=Cons\tan t$- For adiabatic process

$PV=Cons\tan t$Isothermal process

Step :3 Solution :

As we know $PV=nRT$ (ideal gas equation)

$P\propto T/V$

Now the equation for the adiabatic process is :

$P{V}^{\gamma }$ = constant ——$\left(1\right)$

Hence,$(T/V)V^{\gamma }=$ constant

$T{V}^{\gamma -1}$ = constant ——-$\left(2\right)$

Now differentiate equation $\left(2\right)$ w.r.t temp it gives:

$dV/dT=-m$

In the same way as above :

$P{(T/P)}^{\gamma }=$ constant

$V\propto T/P$

$P^{1-\gamma }{T}^{\gamma }=$ constant ——$\left(3\right)$

Now differentiate equation $\left(3\right)$ w.r.t temp it gives:

$dP/dT=(\gamma /1-\gamma )(P/T)$

Hence option A is the correct answer.