Question

Please explain and show all work. Thank you!

Starting from the initial state shown, draw a pV diagram for the three step process: (a) An isochoric process that halves the temperature (b) An isothermal process that halves the (new) pressure (c) An isobaric process that doubles the (new) volume .V

Answer 1

a) Isochoric process (1 to 2 process ) ( Volume remains constant)

$P\propto T$

As temperature is halved from $T_0$ to  $\frac{T_0}{2}$ , pressure is also halved from $P_0$ to $\frac{P_0}{2}$

b) Isothermal process (2 to 3 process ) ( Temperature remains constant )

$P\propto \frac{1}{V}$

As pressure is halved from $\frac{P_0}{2}$ to $\frac{P_0}{4}$ , volume is doubled from $V_0$ to $2V_0$

c) Isobaric process ( 3 to 4 process ) ( Pressure remains constant)

$V\propto T$

Volume is doubled from $2V_0$ to $4V_0$   at constant pressure.