Q. A thermal engine having three moles of mono-atomic gas as its working fluid undergoes the cyclic process as shown in the figure-3.87. Find the mechanical work over one cycle approximately $(R = 8.314\, J/mole-K)$ :

Thermodynamics Report Error

A

40 kJ

B

30 kJ

C

20 kJ

D

10 kJ

Solution:

$W_{12} =W_{34}=0,$ (since the process is isochoric)
$W_{23} =P_{2}\left(V_{3}-V_{2}\right)=n R\left(T_{3}-T_{2}\right),$
$W_{41} =P_{1}\left(V_{2}-V_{4}\right)=n R T\left(T_{1}-T_{4}\right)$
$W =n R\left[T_{3}+T_{1}-T_{2}-T_{4}\right]$
$=3 \times(2400+400-1200-800)+8.314$
$\simeq 20\, kJ$

Questions from Thermodynamics

1. The concept of temperature in thermodynamics is suggested by the

2. 1 g of water is evaporated at 1 atmospheric pressure. Its volume in liquid phase is $1 \,cm ^{3}$ which becomes $1671 \,cm ^{3}$ in the vapour phase. If the latent heat of water is $2256 \,J / g $, then change in its internal energy is

3. One mole of an ideal gas at temperature $T$ was cooled isochorically till the gas pressure fell from $P$ to $\frac{P}{n}$. Then, by an isobaric process, the gas was restored to the initial temperature. The net amount of heat absorbed by the gas in the process is

4. Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and same volume $V$. The mass of the gas in $A$ is $m_{A}$ and that in $B$ is $m_{B}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2 V$. The changes in the pressure in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$ respectively. Then

5. An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cros section $8.0 \times 10^{-3} \, m^2$. Initially the gas is at 300K and occupies a volume of $2.4 \times 10^{-3} \, m^3$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by $0.1\, m$. The force constant of the spring is $8000\, N/m$ and the atmospheric pressure is $1.0 \times 10^5 \, N/m^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be :
(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

JEE Main 2014

Physics Most Viewed Questions

1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

NEET 2021 Physical World, Units and Measurements

2. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

NEET 2020 Dual Nature of Radiation and Matter

3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

NEET 2021 Motion in a Straight Line

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

NEET 2020 Electromagnetic Induction

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$

NEET 2020 Mechanical Properties of Fluids

Latest Updates