Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • An ideal gas is taken from state A (pressure P, volume V) to state B (pressure P/2, volume 2V) along a straight line in the P − V diagram as shown in fig. Then which is incorrect <i

An ideal gas is taken from state A (pressure P, volume V) to state B (pressure P/2, volume 2V) along a straight line in the P − V diagram as shown in fig. Then which is incorrect

Option: 1

The work done by the gas in the process A to B exceeds the work that would be done by it if the system were taken from A to B along the isotherm


Option: 2

In the T-V diagram, the path AB becomes a part of a parabola


Option: 3

In the P-T diagram, the path AB becomes a part of a hyperbola


Option: 4

In going from A to B, the temperature T of the gas first increases to a maximum and then decreases


Answers (1)

best_answer

(a) Work done in process A to B is (see fig.)
\mathrm{W_1} = area of trapezium ABCD

\mathrm{\begin{aligned} & =\left(P+\frac{P}{2}\right) V=\frac{3 P V}{2} \\ & =\frac{3 R T}{2}(\text { for } 1 \text { mole }) \end{aligned}}

If the process A to B were isothermal, the work done would be

\mathrm{W_2=R T \log _e\left(\frac{V_2}{V_1}\right)=R T \log _e(2)=0.69 R T}

\mathrm{\text { Thus } W_1>W_2 \text {. So choice (a) is correct }}

\mathrm{\text { (b) Let } P_0 \text { and } V_0 \text { be the intercepts on the } P \text { and } V \text { axes. }}

The equation of straight line AB is

\mathrm{\begin{aligned} & P=-\frac{P_0}{V_0}\left(V-V_0\right) \\ & \Rightarrow \frac{P}{P_0}+\frac{V}{V_0}=1 \end{aligned}}   ....[1]

\mathrm{\text { Since } P=\frac{R T}{V} \text {, Eq. (1) becomes }}

\mathrm{\frac{R T}{V P_0}+\frac{V}{V_0}=1 \Rightarrow T=\frac{P_0 V}{R}-\frac{P_0 V^2}{R V_0}}

Which represents a parabola on the T-V graph
So choice (b) is also correct

\mathrm{\text { (c) Since } V=\frac{R T}{P} \text {, Eq. (1) becomes }}

\mathrm{\frac{P}{P_0}+\frac{R T}{P V_0}=1 \Rightarrow T=V_0 P-\frac{V_0 P^2}{R P_0}}       ......[2]

Which does not represent a hyperbola. So choice (c) is incorrect
(d) If follows from Eq. (2) above that choice (d) is correct

 

Posted by

Anam Khan

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

MCC NEET UG 2024 Counselling: Special round schedule out; choice filling begins from November 20
anam-khan

Rajasthan NEET UG counselling board cancels MBBS admissions of 100 students at PMCH
anam-khan

100 MBBS students’ fate uncertain as HC reverses ruling on extra seats at Rajasthan private medical college

Latest Question