Question
Explain work done during a thermodynamic process.
✓
Answer
- Consider the system is initially at state A with its pressure is pi and volume is $V_i.$ Let the state be indicated as coordinates $(V_i, p_i)$. It can attain the final state $(V_f, p_f)$ along different possible paths as shown in the p-V diagram below.
- Consider a system that changes its state from initial state A to final state B via path 1 as shown in the figure.
a. When the system changes itself from A to B, both its pressure and volume change. The pressure decreases while volume increases.
b. The work done by the system is given by the area under the curve. It is positive when the volume increases (as shown in the figure) or negative when the volume decreases.
- Consider the system changes its state from A to B via path 2 as shown in figure (a).
a. In this case, the volume increases to $V_i $ from point A up to point C at the constant pressure $p_i.$
b. After point C, the pressure of the system decreases to $p_f $ at constant volume as shown in figure (a).
c. The system thus, reaches its final state B with co-ordinates $(V_f, p_f)$. Work done in this process is represented by the shaded area under the curve in figure (a).
- Consider the system changes its state from A to B via path 3 as shown in figure (b).
Figure (b)
a. In this case, the pressure decreases from $p_i$ to $p_f$ at constant volume $V_i $ along the path AD.
b. After point D, the volume of the system increases to $V_f$ at constant pressure $p_f$ as shown in figure (b). c. Work done in this process is represented by the shaded area under the curve in figure (b). - From figures (a) and (b) we can conclude that the work done is more when the system follows path ACB than the work done by the system along the path ADB.
Thus, the work done by a system in a thermodynamic process depends not only on the initial and the final states but also on the intermediate states, i.e., on the paths along which the change takes place.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
State the expression for the acceleration of a circularly symmetric rigid body rolling without slipping down an inclined plane. Hence, deduce the acceleration of
(i) a ring
(ii) a solid cylinder
(iii) a hollow cylinder
(iv) a solid sphere, rolling without slipping down an inclined plane.
(i) a ring
(ii) a solid cylinder
(iii) a hollow cylinder
(iv) a solid sphere, rolling without slipping down an inclined plane.
Describe Kelvin’s method to determine the resistance of a galvanometer by using a meter bridge.
Find the capacity of a capacitor which when put in series with a $10 \Omega$ resistor makes the power factor equal to $0.5.$ Assume an $80\ V-100\ Hz\ AC$ supply.
→A wooden block of mass m is kept on a piston that can perform vertical vibrations of adjustable frequency and amplitude. During vibrations, we don’t want the block to leave the contact with the piston. How much maximum frequency is possible if the amplitude of vibrations is restricted to $25\ cm$? In this case, how much is the energy per unit mass of the block? $(g ≈ \pi ^2 ≈ 10 m s^{-2})$
→A small drop of mercury oscillates simple harmonically inside a watch glass whose radius of curvature is $2.5 m$. Find the period of the motion. $\left[ g =9.8 m / s ^2\right.$ ]
→With neat labelled diagrams, explain the three lowest modes of vibration of a string stretched between rigid supports.
Explain the effect of a dielectric on the capacitance of a isolated charged parallel-plate capacitor.
Hence, show that if a dielectric of relative permit-tivity (dielectric constant) $k$ completely fills the space between the plates, the capacitance increases by a factor $k$.
→Hence, show that if a dielectric of relative permit-tivity (dielectric constant) $k$ completely fills the space between the plates, the capacitance increases by a factor $k$.
State Boyle's law. Deduce it on the basis of the kinetic theory of an ideal gas.
OR
Deduce Boyle's law using the expression for pressure exerted by an ideal gas.
OR
Deduce Boyle's law using the expression for pressure exerted by an ideal gas.
Why do grinding wheels have large mass and moderate diameter?
What are coherent sources of light?