The figure shows the P-V plot of an ideal gas | vedclass

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

Question

(A) The correct options are $(B)$ and $(D)$.$1$. Analysis of $(A)$: An isothermal process for an ideal gas follows $PV = 	ext{constant}$, which is a

Vedclass · Accepted Answer

$(B,D)$

Vedclass · Answer

(A) The correct options are $(B)$ and $(D)$.$1$. Analysis of $(A)$: An isothermal process for an ideal gas follows $PV = 	ext{constant}$, which is a rectangular hyperbola on a $P-V$ diagram, not a circular or elliptical arc. Thus, $(A)$ is incorrect.$2$. Analysis of $(B)$: For the path $B ightarrow C ightarrow D$, the volume decreases ($V$ goes from $3$ to $1$), so the work done by the gas $W = \int P \, dV$ is negative. Also, the temperature $T \propto PV$ decreases from $B$ to $C$ and $C$ to $D$ (as $P$ and $V$ both decrease or stay low), so the change in internal energy $\Delta U$ is negative. From the first law of thermodynamics, $\Delta Q = \Delta U + W$. Since both $\Delta U $3$. Analysis of $(C)$: The work done during $A ightarrow B ightarrow C$ is the area under the curve $ABC$ with the $V$-axis. Since the path $A ightarrow B ightarrow C$ involves expansion followed by compression, the net work is the area under the curve, which is clearly non-zero. Thus, $(C)$ is incorrect.$4$. Analysis of $(D)$: The cycle $ABCDA$ is traversed in a clockwise direction on the $P-V$ diagram. For a clockwise cycle, the net work done by the gas is positive, equal to the area enclosed by the cycle. Thus, $(D)$ is correct.

Similar Questions

For a gas with adiabatic index $\gamma = 5/3$,what percentage of heat supplied at constant pressure is converted into work (in $\%$)?

Given $P_A = 3 \times 10^4 \, Pa$,$P_B = 8 \times 10^4 \, Pa$,$V_A = 2 \times 10^{-3} \, m^3$,and $V_D = 5 \times 10^{-3} \, m^3$. An ideal gas absorbs $600 \, J$ of heat in the process $AB$ and $200 \, J$ of heat in the process $BC$. Find the change in internal energy between $A$ and $C$ in $J$.

The $P-V$ diagram of a certain process (Carnot cycle) is as shown. The process is also represented as:

$10,000$ small balls,each of mass $1 \, g$,strike a surface of area $1 \, cm^2$ per second with a velocity of $100 \, m/s$ perpendicular to the surface. They rebound with the same velocity. What is the pressure exerted on the surface?

An ideal gas with adiabatic exponent $(\gamma = 1.5)$ undergoes a process in which the work done by the gas is equal to the increase in the internal energy of the gas. The molar heat capacity of the gas for this process is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module