Advertisements
Advertisements
प्रश्न
derive the relation between the change in internal energy (∆U), work is done (W), and heat (Q).
Advertisements
उत्तर
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
संबंधित प्रश्न
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)
A steam engine delivers 5.4×108 J of work per minute and services 3.6 × 109 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?
The outer surface of a cylinder containing a gas is rubbed vigorously by a polishing machine. The cylinder and its gas become warm. Is the energy transferred to the gas heat or 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.
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 ?
When a tyre bursts, the air coming out is cooler than the surrounding air. Explain.
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.
The pressure p and volume V of an ideal gas both increase in a process.
(a) Such a process is not possible.
(b) The work done by the system is positive.
(c) The temperature of the system must increase.
(d) Heat supplied to the gas is equal to the change in internal energy.
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.
Which of the following system freely allows the exchange of energy and matter with its environment?
What is the energy associated with the random, disordered motion of the molecules of a system called as?
When does a system lose energy to its surroundings and its internal energy decreases?
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.
A cylinder containing one gram molecule of the gas was compressed adiabatically until its temperature rose from 27°C to 97°C. Calculate the work done and heat produced in the gas (𝛾 = 1.5).
In a thermodynamic system, working substance is ideal gas. Its internal energy is in the form of ______.
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 ______.
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 thermodynamics, heat and work are ______.
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:
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 ______.
A cyclic process ABCA is shown in the V-T diagram. A process on the P-V diagram is ______.
The internal energy of one mole of argon at 300 K is ______. (R = 8.314 J/mol.K)
What is heat?
A system releases 125 kJ of heat while 104 kJ work is done on the system. Calculate the change in internal energy.
Explain the change in internal energy of a thermodynamic system (the gas) by heating it.
