An ideal gas initially at state with pressure and volume is taken to state with…

PHYSICS · Multi-part · CBSE · Physics · Thermodynamics · Thermodynamics

Problem

An ideal gas initially at state

A

with pressure

P_1

and volume

V_1

is taken to state

B

with pressure

P_2

and volume

V_2

(

P_1V_1 = P_2V_2

) by the following two-step path: • Step 1: a slow isothermal expansion at temperature

T

from

V_1

V_2

. • Step 2: cooling at constant volume

V_2

until the pressure falls from

P_2

P_3

. Answer the questions below. Assume one mole of gas. (i) Derive an expression for the work done in step 1 in terms of

R,\,T,\,V_1

, and

V_2

. (ii) Show that the work done in step 2 is zero without performing any integration. (iii) Sketch a clearly labelled

P

–

V

diagram for the complete process and shade the region that represents the total work done by the gas. (iv) Given that

V_2 = 2V_1

and

T = 400\,\text{K}

, calculate the numerical value of the total work done. Take

R = 8.314\,\text{J mol}^{-1}\text{K}^{-1}