An ideal gas undergoes a process A rightarrow | vedclass

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

Question

(B) For an adiabatic process, the relation between pressure $p$ and volume $V$ is given by $p V^\gamma = 	ext{constant}$.For the adiabatic process $A

Vedclass · Accepted Answer

$\frac{p_0 V_0(2^{1/\gamma}-2)}{1-\gamma}$

Vedclass · Answer

(B) For an adiabatic process, the relation between pressure $p$ and volume $V$ is given by $p V^\gamma = 	ext{constant}$.For the adiabatic process $A ightarrow B$, the states are $(2p_0, V_0)$ and $(p_0, V_1)$.Thus, $(2p_0) V_0^\gamma = p_0 V_1^\gamma$.Dividing by $p_0$, we get $2 V_0^\gamma = V_1^\gamma$, which implies $V_1 = 2^{1/\gamma} V_0$.The work done $W$ in an adiabatic process is given by $W = \frac{p_i V_i - p_f V_f}{\gamma - 1}$.Substituting the values for process $A ightarrow B$:$W = \frac{(2p_0)(V_0) - (p_0)(V_1)}{\gamma - 1} = \frac{2p_0 V_0 - p_0 (2^{1/\gamma} V_0)}{\gamma - 1}$.Rearranging the terms, we get $W = \frac{p_0 V_0 (2 - 2^{1/\gamma})}{\gamma - 1} = \frac{p_0 V_0 (2^{1/\gamma} - 2)}{1 - \gamma}$.

An ideal gas undergoes a process $A \rightarrow B \rightarrow C \rightarrow A$ cycle. The process $A \rightarrow B$ is adiabatic. Calculate the work done in the process $A \rightarrow B$.

Similar Questions

$A$ gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$

$A$ mixture of gases at $STP$ for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{9}$th of its original volume. The final temperature of the mixture is .......... $^{\circ}C$.

For an ideal gas,the internal energy is given by $U = 5pV/2 + C$,where $C$ is a constant. The equation of the adiabats in the $pV$-plane will be

For an adiabatic process with $\gamma = 2.5$,if the volume of a gas is reduced to $1/8$ of its initial volume,what will be the new pressure $P'$ in terms of the initial pressure $P$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module