Answer
Verified
385.5k+ views
Hint: The product of pressure and volume is represented by an area on the p-v diagram. The area under this curve tells us the work done during a thermodynamic process. In this process it can be found out by calculating the area of the curve this is a simple and quick method.
The curve showing the variation of volume of a substance along the x-axis and the variation of the pressure along the y-axis is the P-V diagram.
In this question first, find the total change in volume along the x-axis and change in pressure along the y-axis and then find the work done under the curve.
Complete step by step solution:
Given that the gas is going through the curve ABCA
Where the change in volume takes place from \[2 \times {10^{ - 3}}{m^3}\]to \[7 \times {10^{ - 3}}{m^3}\]along positive x-axis and pressure changes from \[2 \times {10^5}Pa\] to \[6 \times {10^5}Pa\] along the y-direction.
Hence,
\[\vartriangle V = 5 \times {10^{ - 3}}{m^3}\]
\[\vartriangle P = 4 \times {10^5}Pa\]
So the area under the curve for the total work done will be equal to
Net work is done = area under the curve A B C
\[
W = \dfrac{1}{2} \times 5 \times {10^{ - 3}} \times 4 \times {10^5} \\
= \dfrac{1}{2} \times 5 \times 4 \times {10^2} \\
= 10 \times {10^2} \\
= 1000J \\
\]
Hence the total work is done by the gas under the curve =1000J
Option (B) is correct.
Note: Students should be careful in some cases where in some cases specific volume is plotted along the x-axis instead of volume; in such cases area under the curve represents work per unit mass of the working fluid given as J/Kg.
The curve showing the variation of volume of a substance along the x-axis and the variation of the pressure along the y-axis is the P-V diagram.
In this question first, find the total change in volume along the x-axis and change in pressure along the y-axis and then find the work done under the curve.
Complete step by step solution:
Given that the gas is going through the curve ABCA
Where the change in volume takes place from \[2 \times {10^{ - 3}}{m^3}\]to \[7 \times {10^{ - 3}}{m^3}\]along positive x-axis and pressure changes from \[2 \times {10^5}Pa\] to \[6 \times {10^5}Pa\] along the y-direction.
Hence,
\[\vartriangle V = 5 \times {10^{ - 3}}{m^3}\]
\[\vartriangle P = 4 \times {10^5}Pa\]
So the area under the curve for the total work done will be equal to
Net work is done = area under the curve A B C
\[
W = \dfrac{1}{2} \times 5 \times {10^{ - 3}} \times 4 \times {10^5} \\
= \dfrac{1}{2} \times 5 \times 4 \times {10^2} \\
= 10 \times {10^2} \\
= 1000J \\
\]
Hence the total work is done by the gas under the curve =1000J
Option (B) is correct.
Note: Students should be careful in some cases where in some cases specific volume is plotted along the x-axis instead of volume; in such cases area under the curve represents work per unit mass of the working fluid given as J/Kg.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE