Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

A piston-cylinder device contains 2 kg of water at $200^{\circ} \mathrm{C}$ and 1 MPa. The water undergoes an isentropic compression to a final state where the specific volume is $0.1 \mathrm{~m}^3 / \mathrm{kg}$ . Calculate the final temperature of the water in ${ }^{\circ} \mathrm{C}$ .

Given: Initial temperature $\mathrm{(T_{1})}$ = 200 C
Initial pressure $\mathrm{(P_{1})}$ = 1 MP a
Specific volume $\mathrm{(V_{2})}$ = 0.1 m/kg
The process is isentropic for water.
The specific heat capacity at constant pressure $\mathrm{(C_{p})}$ for water is approximately 4.18 kJ/(kgK).
Option: 1
300 C

Option: 2
200 C

Option: 3
400 C

Option: 4
500 C

Answers (1)

best_answer

Since the process is isentropic, we know that the entropy (s) remains constant during the compression:

$\mathrm{s_1=s_2}$

The entropy change during the process is given by:

$\mathrm{\Delta s=s_2-s_1=0}$

The entropy change of a substance during an isentropic process can be approximated using the specific heat capacity at constant pressure $\mathrm{(C_{p})}$ :

$\mathrm{\Delta s=C_p \ln \left(\frac{T_2}{T_1}\right)=0}$

Rearranging the equation and solving for the final temperature $\left ( \mathrm{{T_2}} \right )$ :

$\mathrm{T_2=T_1 \cdot \exp \left(-\frac{\Delta s}{C_p}\right)}$

Substitute the given values:

$\mathrm{T_1=200 C=473.15 \mathrm{~K}}$

Calculating the value of $\mathrm{T_2}$ :

$\mathrm{T_2=473.15 \cdot \exp (0)=473.15 \mathrm{~K} \approx 200 \mathrm{C}}$

Answer: The final temperature of the water is approximately 200 C.

So, correct option is (2), 200 C

Posted by

Gaurav

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

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions

anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question