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The internal energy of a gas obeying van der Waals, equation (p + a/V2)(V - b) = RT depends on its
- a)Temperature
- b)temperature and pressure
- c)temperature and specific volume
- d)pressure and specific volume
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The internal energy of a gas obeying van der Waals, equation (p + a/V2...
internal energy: U = u (T, V)
For a real gas, the internal energy if a function of both the temperature and the specific volume.
That is,
U = f(T,u)
For ideal gas (∂U/∂V)T = 0
∴ U = U (T) only
Important Points
For an ideal gas (no intermolecular interactions and no molecular volume), appropriate equation of state would be: PV = nRT ⇒ V = nRT/P i.e. V = f(T,P,n)
There are many equations of state describing real gases. These equations take in consideration molecular volume and interactions. The most well-known such equation is the Van der Waals equation.
The internal energy of an ideal gas is a function of temperature only and is independent of pressure and volume. u = u(T)
Most Upvoted Answer
The internal energy of a gas obeying van der Waals, equation (p + a/V2...
Internal Energy of a Gas obeying van der Waals Equation
The van der Waals equation of state is an improvement over the ideal gas equation by considering the intermolecular forces and the finite size of gas molecules. It is given by:
(p + a/V^2)(V - b) = RT
where:
p is the pressure of the gas
V is the volume of the gas
a and b are constants related to the attractive and repulsive forces between molecules
R is the ideal gas constant
T is the temperature of the gas
Factors affecting the Internal Energy
The internal energy of a gas is the sum of the kinetic and potential energies of its molecules. In the case of a gas obeying the van der Waals equation, the internal energy depends on the temperature and specific volume.
Temperature
Temperature is a measure of the average kinetic energy of the gas molecules. As the temperature increases, the kinetic energy of the molecules also increases. This leads to an increase in the internal energy of the gas.
Specific Volume
Specific volume is the volume occupied by a unit mass of the gas. In the van der Waals equation, the term (V - b) represents the effective volume available for the gas molecules to move around. The constant b accounts for the volume occupied by the gas molecules themselves.
As the specific volume decreases (i.e., the gas becomes more compressed), the available volume for the gas molecules to move decreases. This results in an increase in the potential energy of the gas molecules and hence an increase in the internal energy.
Conclusion
In conclusion, the internal energy of a gas obeying the van der Waals equation depends on both the temperature and specific volume. The temperature affects the kinetic energy of the gas molecules, while the specific volume affects the potential energy of the gas molecules. Both of these factors contribute to the overall internal energy of the gas.
The van der Waals equation of state is an improvement over the ideal gas equation by considering the intermolecular forces and the finite size of gas molecules. It is given by:
(p + a/V^2)(V - b) = RT
where:
p is the pressure of the gas
V is the volume of the gas
a and b are constants related to the attractive and repulsive forces between molecules
R is the ideal gas constant
T is the temperature of the gas
Factors affecting the Internal Energy
The internal energy of a gas is the sum of the kinetic and potential energies of its molecules. In the case of a gas obeying the van der Waals equation, the internal energy depends on the temperature and specific volume.
Temperature
Temperature is a measure of the average kinetic energy of the gas molecules. As the temperature increases, the kinetic energy of the molecules also increases. This leads to an increase in the internal energy of the gas.
Specific Volume
Specific volume is the volume occupied by a unit mass of the gas. In the van der Waals equation, the term (V - b) represents the effective volume available for the gas molecules to move around. The constant b accounts for the volume occupied by the gas molecules themselves.
As the specific volume decreases (i.e., the gas becomes more compressed), the available volume for the gas molecules to move decreases. This results in an increase in the potential energy of the gas molecules and hence an increase in the internal energy.
Conclusion
In conclusion, the internal energy of a gas obeying the van der Waals equation depends on both the temperature and specific volume. The temperature affects the kinetic energy of the gas molecules, while the specific volume affects the potential energy of the gas molecules. Both of these factors contribute to the overall internal energy of the gas.
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The internal energy of a gas obeying van der Waals, equation (p + a/V2)(V - b) = RT depends on itsa)Temperatureb)temperature and pressurec)temperature and specific volumed)pressure and specific volumeCorrect answer is option 'C'. Can you explain this answer?
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