Advertisements
Advertisements
Question
derive the relation between the change in internal energy (∆U), work is done (W), and heat (Q).
Advertisements
Solution
Relation between the change in internal energy (ΔU), work is done (W), and heat (Q):
- When the amount of heat Q is added to the system and the system does not do any work during the process, its internal energy increases by the amount, ΔU = Q.
- When the system does some work to increase its volume, and no heat is added to it while expanding, the system loses energy to its surrounding,s and its internal energy decreases.
∴ ΔU = –W. - As the internal energy can be changed using both ways, we can consider the total change in the internal energy as,
ΔU = Q – W ….(1)
This is the mathematical statement of the first law of thermodynamics.
APPEARS IN
RELATED QUESTIONS
Explain why Air pressure in a car tyre increases during driving.
Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
Do the intermediate states of the system (before settling to the final equilibrium state) lie on its P-V-T surface?
A force F is applied on a block of mass M. The block is displaced through a distance d in the direction of the force. What is the work done by the force on the block? Does the internal energy change because of this work?
When we rub our hands they become warm. Have we supplied heat to the hands?
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.
The final volume of a system is equal to the initial volume in a certain process. Is the work done by the system necessarily zero? Is it necessarily nonzero?
An ideal gas is pumped into a rigid container having diathermic walls so that the temperature remains constant. In a certain time interval, the pressure in the container is doubled. Is the internal energy of the contents of the container also doubled in the interval ?
Consider the following two statements.
(A) If heat is added to a system, its temperature must increase.
(B) If positive work is done by a system in a thermodynamic process, its volume must increase.
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.
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?
Figure shows a cylindrical tube of volume V with adiabatic walls containing an ideal gas. The internal energy of this ideal gas is given by 1.5 nRT. The tube is divided into two equal parts by a fixed diathermic wall. Initially, the pressure and the temperature are p1, T1 on the left and p2, T2 on the right. The system is left for sufficient time so that the temperature becomes equal on the two sides. (a) How much work has been done by the gas on the left part? (b) Find the final pressures on the two sides. (c) Find the final equilibrium temperature. (d) How much heat has flown from the gas on the right to the gas on the left?
A mixture of fuel and oxygen is burned in a constant-volume chamber surrounded by a water bath. It was noticed that the temperature of water is increased during the process. Treating the mixture of fuel and oxygen as the system,
- Has heat been transferred?
- Has work been done?
- What is the sign of ∆U?
A system releases 130 kJ of heat while 109 kJ of work is done on the system. Calculate the change in internal energy.
What is the energy associated with the random, disordered motion of the molecules of a system called as?
What is the internal energy of the system, when the amount of heat Q is added to the system and the system does not do any work during the process?
When does a system lose energy to its surroundings and its internal energy decreases?
Explain the different ways through which the internal energy of the system can be changed.
One gram of water (1 cm3) becomes 1671 cm3 of steam at a pressure of 1 atm. The latent heat of vaporization at this pressure is 2256 J/g. Calculate the external work and the increase in internal energy.
In a thermodynamic system, working substance is ideal gas. Its internal energy is in the form of ______.
Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
What is the change in the temperature of the gas?
In insulated systems, the amount of external work done by the gas is proportional to:
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 ______.
An expansion process on a diatomic ideal gas (Cv = 5/2 R), has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are: the pressure is 300 kPa, the volume is 0.08 m3 and the temperature is 390 K. The final pressure is 90 kPa and the final temperature s 320 K. The change in the internal energy of the gas, in SI units, is closest to:
The molar specific heat of He at constant volume is 12.47 J/mol.K. Two moles of He are heated at constant pressure. So the rise in temperature is 10 K. Find the increase in internal energy of the gas.
Explain the change in internal energy of a thermodynamic system (the gas) by heating it.
