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 Two bodies at different temperatures T1 and T2, if brought in thermal contact, do not necessarily settle to the mean temperature (T1 + T2)/2.
Explain why Air pressure in a car tyre increases during driving.
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?
Can work be done by a system without changing its volume?
Figure shows two processes A and B on a system. Let ∆Q1 and ∆Q2 be the heat given to the system in processes A and B respectively. Then ____________ .
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.
An ideal gas goes from the state i to the state f as shown in figure. The work done by the gas during the process ______________ .
A gas is contained in a metallic cylinder fitted with a piston. The piston is suddenly moved in to compress the gas and is maintained at this position. As time passes the pressure of the gas in the cylinder ______________ .
A gas is taken through a cyclic process ABCA as shown in figure. If 2.4 cal of heat is given in the process, what is the value of J ?
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?
Which of the following is correct, when the energy is transferred to a system from its environment?
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?
Explain given cases related to energy transfer between the system and surrounding –
- energy transferred (Q) > 0
- energy transferred (Q) < 0
- energy transferred (Q) = 0
The internal energy of a system is ______
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?
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:
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)
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.
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.
