Advertisements
Advertisements
Question
A gas is initially at a pressure of 100 kPa and its volume is 2.0 m3. Its pressure is kept constant and the volume is changed from 2.0 m3 to 2.5 m3. Its Volume is now kept constant and the pressure is increased from 100 kPa to 200 kPa. The gas is brought back to its initial state, the pressure varying linearly with its volume. (a) Whether the heat is supplied to or extracted from the gas in the complete cycle? (b) How much heat was supplied or extracted?
Advertisements
Solution
(a) Given:-
P1 = 100 kPa,
V1 = 2 m3
V2 = 2.5 m3
∆V = 0.5 m3
Work done, W = P∆V
\[W = 100 \times {10}^3 \times 0 . 5\]
\[W = 5 \times {10}^4 J\]
WAB = Area under line AB = 5 × 104 J
If volume is kept constant for line BC, then ∆V = 0.
WBC = P∆V = 0
Work done while going from point B to C = 0
When the system comes back to the initial point A from C, work done is equal to area under line AC.
WCA = Area of triangle ABC + Area of rectangle under line AB
Total work done, W = Area enclosed by the ABCA
W = WAC - WAB
From the graph, we see that the area under AC is greater than the area under AB. We also see that heat is extracted from the system as change in the internal energy is zero.
(b) Amount of heat extracted = Area enclosed under ABCA
\[= \frac{1}{2} \times 0 . 5 \times 100 \times {10}^3 = 25000 J\]
APPEARS IN
RELATED QUESTIONS
In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal, how much is the net work done by the system in the latter case? (Take 1 cal = 4.19 J)
Should the internal energy of a system necessarily increase if heat is added to it?
A closed bottle contains some liquid. the bottle is shaken vigorously for 5 minutes. It is found that the temperature of the liquid is increased. Is heat transferred to the liquid? Is work done on the liquid? Neglect expansion on heating.
Consider two processes on a system as shown in figure.
The volumes in the initial states are the same in the two processes and the volumes in the final states are also the same. Let ∆W1 and ∆W2 be the work done by the system in the processes A and B respectively.
In a process on a system, the initial pressure and volume are equal to the final pressure and volume.
(a) The initial temperature must be equal to the final temperature.
(b) The initial internal energy must be equal to the final internal energy.
(c) The net heat given to the system in the process must be zero.
(d) The net work done by the system in the process must be zero.
A 100 kg lock is started with a speed of 2.0 m s−1 on a long, rough belt kept fixed in a horizontal position. The coefficient of kinetic friction between the block and the belt is 0.20. (a) Calculate the change in the internal energy of the block-belt system as the block comes to a stop on the belt. (b) Consider the situation from a frame of reference moving at 2.0 m s−1 along the initial velocity of the block. As seen from this frame, the block is gently put on a moving belt and in due time the block starts moving with the belt at 2.0 m s−1. calculate the increase in the kinetic energy of the block as it stops slipping past the belt. (c) Find the work done in this frame by the external force holding the belt.
A substance is taken through the process abc as shown in figure. If the internal energy of the substance increases by 5000 J and a heat of 2625 cal is given to the system, calculate the value of J.
An ideal gas is compressed at a constant temperature. Its internal energy will ____________.
In a thermodynamic system, working substance is ideal gas. Its internal energy is in the form of ______.
8 m3 of a gas is heated at the pressure 105 N/m2 until its volume increases by 10%. Then, the external work done by the gas is ____________.
When 1 g of water at 0° C and 1 x 105 N/m2 pressure is converted into ice of volume 1.082 cm3, the external work done will be ____________.
Two samples A and B, of a gas at the same initial temperature and pressure are compressed from volume V to V/2; A isothermally and B adiabatically. The final pressure of A will be ______.
Which of the following represents isothermal process?
Figure shows the P-V diagram of an ideal gas undergoing a change of state from A to B. Four different parts I, II, III and IV as shown in the figure may lead to the same change of state.
- Change in internal energy is same in IV and III cases, but not in I and II.
- Change in internal energy is same in all the four cases.
- Work done is maximum in case I
- Work done is minimum in case II.
n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes:
A `→` B: Isothermal expansion at temperature T so that the volume is doubled from V1 to V2 = 2V1 and pressure changes from P1 to P2.
B `→` C: Isobaric compression at pressure P2 to initial volume V1.
C `→` A: Isochoric change leading to change of pressure from P2 to P1.
Total workdone in the complete cycle ABCA is ______.
In thermodynamics, heat and work are ______.
A gas is compressed at a constant pressure of 50 N/m2 from a volume of 10 m3 to a volume of 4 m3. Energy of 100 J is then added to the gas by heating. Its internal energy is ______.
The internal energy of one mole of argon is ______.
What is heat?
Explain the change in internal energy of a thermodynamic system (the gas) by heating it.
