In the following p-V diagram,the equation of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The work done in a closed $p-V$ cycle is equal to the area enclosed by the path. Since the cycle is traversed in a counter-clockwise direction,the

Vedclass · Accepted Answer

$-\frac{1}{3a}$

Vedclass · Answer

(D) The work done in a closed $p-V$ cycle is equal to the area enclosed by the path. Since the cycle is traversed in a counter-clockwise direction,the work done by the gas is negative.The area under the curve $(V-2)^2 = 4aP$ from $V=1$ to $V=3$ is given by $\int_{1}^{3} P \, dV$.From the equation,$P = \frac{(V-2)^2}{4a}$.Area under the curve $= \int_{1}^{3} \frac{(V-2)^2}{4a} \, dV = \frac{1}{4a} \left[ \frac{(V-2)^3}{3} ight]_{1}^{3} = \frac{1}{12a} [(3-2)^3 - (1-2)^3] = \frac{1}{12a} [1 - (-1)] = \frac{2}{12a} = \frac{1}{6a}$.At $V=1$ or $V=3$,the pressure $P_0$ is given by $(1-2)^2 = 4aP_0$,so $P_0 = \frac{1}{4a}$.The area of the rectangle formed by the top horizontal line (at $P_0$) and the $V$-axis from $V=1$ to $V=3$ is $P_0 	imes (3-1) = \frac{1}{4a} 	imes 2 = \frac{1}{2a}$.The area enclosed by the cycle is the area of the rectangle minus the area under the curve:Area $= \frac{1}{2a} - \frac{1}{6a} = \frac{3-1}{6a} = \frac{2}{6a} = \frac{1}{3a}$.Since the cycle is counter-clockwise,the work done $W = -\frac{1}{3a}$.

In the following $p-V$ diagram,the equation of state along the curved path is given by $(V-2)^2 = 4aP$,where $a$ is a constant. The total work done in the closed path is:

Similar Questions

$A$ thermodynamic system is taken from state $A$ to $B$ along $ACB$ and is brought back to $A$ along $BDA$ as shown in the $PV$ diagram. The net work done during the complete cycle is given by the area

$A$ thermodynamic system is taken through the cycle $PQRSP$ as shown in the $P-V$ diagram. The net work done by the system is ....... $J$.

$A$ gas is taken through a cyclic process $ABCA$ as shown in the figure. If $2.4 \, cal$ of heat is given in the process,what is the value of $J$ in $J/cal$ (mechanical equivalent of heat)?

$A$ thermodynamic system undergoes a cyclic process $ABC$ as shown in the diagram. The work done by the system per cycle is (in $J$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module