The figure shows a cylindrical adiabatic cont | vedclass

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

Question

(D) Let the final equilibrium temperature be $T$. Since the container is adiabatic and the piston is conducting,heat flows from the hotter side to the

Vedclass · Accepted Answer

$\frac{6}{5}P_0 A$

Vedclass · Answer

(D) Let the final equilibrium temperature be $T$. Since the container is adiabatic and the piston is conducting,heat flows from the hotter side to the colder side until equilibrium is reached. The total internal energy of the system remains constant.Using the ideal gas law $PV = nRT$,the number of moles in each part is $n_L = \frac{P_0 V_0}{R(4T_0)}$ and $n_R = \frac{P_0 V_0}{RT_0}$.Since the total internal energy is conserved:$n_L C_V (4T_0 - T) = n_R C_V (T - T_0)$$\frac{P_0 V_0}{4RT_0} (4T_0 - T) = \frac{P_0 V_0}{RT_0} (T - T_0)$$\frac{4T_0 - T}{4} = T - T_0$$4T_0 - T = 4T - 4T_0$$8T_0 = 5T \implies T = \frac{8}{5}T_0$Since the piston is free to move but held at rest by an external force,the volumes remain $V_0$ in each part. The final pressures are:$P_{L,f} = \frac{n_L RT}{V_0} = \frac{P_0 V_0}{4RT_0} \cdot \frac{R(8T_0/5)}{V_0} = \frac{2}{5}P_0$$P_{R,f} = \frac{n_R RT}{V_0} = \frac{P_0 V_0}{RT_0} \cdot \frac{R(8T_0/5)}{V_0} = \frac{8}{5}P_0$The external force $F$ required to keep the piston at rest is:$F = (P_{R,f} - P_{L,f})A = (\frac{8}{5}P_0 - \frac{2}{5}P_0)A = \frac{6}{5}P_0 A$

List-$I$	List-$II$
$A$. Pressure varies inversely with volume of an ideal gas.	$I$. Adiabatic process
$B$. Heat absorbed goes partly to increase internal energy and partly to do work.	$II$. Isochoric process
$C$. Heat is neither absorbed nor released by a system.	$III$. Isothermal process
$D$. No work is done on or by a gas.	$IV$. Isobaric process

Similar Questions

The internal energy of the air in a room of volume $V$ at temperature $T$, with outside pressure $P$ increasing linearly with time, varies as

An ideal gas with constant heat capacity $C_V = \frac{3}{2} n R$ is made to carry out a cycle that is depicted by a triangle in the figure given below. The following statement is true about the cycle.

$A$ thermodynamic cycle of an ideal gas is shown in the figure. Choose the correct option which represents the same cycle.

$A$ gas undergoes a change of state during which $100 \ J$ of heat is supplied to it and it does $20 \ J$ of work. The system is brought back to its original state through a process during which $20 \ J$ of heat is released by the gas. The work done by the gas in the second process is ....... $J$

Vedclass Test Series

Exam Paper Generator

Online Exam Module