Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Calculate the entropy change when 5 moles of a monatomic ideal gas undergoes an isothermal expansion from an initial volume of 8 liters to a final volume of 40 liters. The initial temperature is $300 \mathrm{~K}$ .

Option: 1
$15 \mathrm{~J} / \mathrm{K}$

Option: 2
$13.38 \mathrm{~J} / \mathrm{K}$

Option: 3
$14.8 \mathrm{~J} / \mathrm{K}$

Option: 4
$19 \mathrm{~J} / \mathrm{K}$

Answers (1)

Step 1: Use the adiabatic process to relate the initial and final conditions for an ideal gas.
$\mathrm{ P_1 V_1^\gamma=P_2 V_2^\gamma }$

Given: Number of moles, $\mathrm{n=5}$ moles Initial volume, $\mathrm{V_1=8}$ liters Final volume, $\mathrm{V_2=40}$ liters Initial temperature, $\mathrm{T_1=300 \mathrm{~K}}$

Specific heat ratio (adiabatic index), $\mathrm{\gamma=\frac{C_p}{C_v}}$ , typically for monatomic gases $\mathrm{\gamma \approx 1.4}$

Step 2: Calculate the initial and final pressures using the adiabatic process equation.

$\mathrm{ P_1=\frac{n R T_1}{V_1} }$

$\mathrm{ P_2=\frac{n R T_2}{V_2}}$

Step 3: Use the relation between pressure and volume in an adiabatic process to find the temperature at the final state.

$\mathrm{ T_2=\frac{P_2 V_2}{n R} }$

Step 4: Calculate the change in entropy $\mathrm{ (\Delta S) }$ for an isothermal process using the ideal gas equation.
$\mathrm{ \Delta S=R \ln \left(\frac{V_2}{V_1}\right) }$
Step 5: Substitute the values and calculate the entropy change.

$\mathrm{ \Delta S=R \ln \left(\frac{40}{8}\right) \\ }$

$\mathrm{ \Delta S=13.38 J / K }$

So,correct option is 2.

Posted by

Kshitij

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_b of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75

Trending Articles/News

anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 applications close on November 27; apply at jeemain.nta.nic.in

anam-khan

JEE 2026: IIT admissions show major shift toward AI, data science, away from core engineering courses

anam-khan

JEE Main 2026: NIT Delhi cut-offs for BTech courses show ever-increasing demands for AI, computer skills

Latest Question