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In a thermodynamic system, ∆u represents an increase in its internal energy and ∆W work done by the system. Which of the following statements is true?
- a)∆u = ∆W in an isothermal process
- b)∆u = ∆W in an adiabatic process
- c)∆u = -∆W in an isothermal process
- d)∆u = -∆W in an adiabatic process
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In a thermodynamic system, u represents an increase in its internal en...
Explanation:
Internal Energy:
Internal energy is the sum of all forms of energy present in a system. It includes the kinetic energy of molecules, potential energy of molecules due to their position, and the energy of intermolecular forces.
ΔU = Q + W
where ΔU is the change in internal energy, Q is the heat absorbed by the system and W is the work done by the system.
Work Done:
Work done by the system is the energy transferred from the system to the surroundings. It is calculated as the product of force and displacement in the direction of force.
W = -PΔV
where P is the pressure and ΔV is the change in volume.
Adiabatic Process:
An adiabatic process is a process that occurs without the transfer of heat between the system and the surroundings. Thus, the heat absorbed by the system is zero.
ΔU = W
As there is no heat transfer, Q = 0. Thus, the equation reduces to ΔU = W. Hence, u = -W in an adiabatic process.
Isothermal Process:
An isothermal process is a process that occurs at a constant temperature. As the temperature is constant, there is no change in the internal energy of the system.
ΔU = 0
As ΔU = 0, the equation reduces to Q = -W. Hence, u = -W in an isothermal process.
Conclusion:
Therefore, option D is the correct answer.
Internal Energy:
Internal energy is the sum of all forms of energy present in a system. It includes the kinetic energy of molecules, potential energy of molecules due to their position, and the energy of intermolecular forces.
ΔU = Q + W
where ΔU is the change in internal energy, Q is the heat absorbed by the system and W is the work done by the system.
Work Done:
Work done by the system is the energy transferred from the system to the surroundings. It is calculated as the product of force and displacement in the direction of force.
W = -PΔV
where P is the pressure and ΔV is the change in volume.
Adiabatic Process:
An adiabatic process is a process that occurs without the transfer of heat between the system and the surroundings. Thus, the heat absorbed by the system is zero.
ΔU = W
As there is no heat transfer, Q = 0. Thus, the equation reduces to ΔU = W. Hence, u = -W in an adiabatic process.
Isothermal Process:
An isothermal process is a process that occurs at a constant temperature. As the temperature is constant, there is no change in the internal energy of the system.
ΔU = 0
As ΔU = 0, the equation reduces to Q = -W. Hence, u = -W in an isothermal process.
Conclusion:
Therefore, option D is the correct answer.
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Community Answer
In a thermodynamic system, u represents an increase in its internal en...
Isothermal process- a process in which temperature is constant.
Adiabatic process- a process in which there is no transfer of heat ( q=0)
We know, by the first law of thermodynamics, ∆u = q - ∆w
since q=0 in an adiabatic process, the change in internal energy ∆u will be equal to work done by the system, -∆w
Explanation for the the other options:-
a) This statement is not true, because we know the internal energy of a system depends on the avergae kinetic energy of the particles in the system => temperature. There is no change in temperature in an isothermal process, resulting in no change in the internal energy.
b) The equation is U= q - w in terms of chemistry. So if we take into account the signs, this option is incorrect.
c) The same explanation as for option a. There is. no change in internal energy in an isothermal process.
{The answers are given in the theory of ideal gas. Change in internal energy for real gases may or may not be 0 in an isothermal process.}
Adiabatic process- a process in which there is no transfer of heat ( q=0)
We know, by the first law of thermodynamics, ∆u = q - ∆w
since q=0 in an adiabatic process, the change in internal energy ∆u will be equal to work done by the system, -∆w
Explanation for the the other options:-
a) This statement is not true, because we know the internal energy of a system depends on the avergae kinetic energy of the particles in the system => temperature. There is no change in temperature in an isothermal process, resulting in no change in the internal energy.
b) The equation is U= q - w in terms of chemistry. So if we take into account the signs, this option is incorrect.
c) The same explanation as for option a. There is. no change in internal energy in an isothermal process.
{The answers are given in the theory of ideal gas. Change in internal energy for real gases may or may not be 0 in an isothermal process.}
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In a thermodynamic system, u represents an increase in its internal energy and W work done by the system. Which of the following statements is true?a)u = W in an isothermal processb)u = W in an adiabatic processc)u = -W in an isothermal processd)u = -W in an adiabatic processCorrect answer is option 'D'. Can you explain this answer?
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