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When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas, is
- a)2/5
- b)3/5
- c)3/7
- d)5/7
Correct answer is option 'D'. Can you explain this answer?
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Heat energy supplied to an ideal diatomic gas can be used to increase its internal energy and to do work. When the gas is heated at constant pressure, the heat energy supplied is used to increase its internal energy. The fraction of heat energy supplied which increases the internal energy of the gas is given by the formula:
Fraction of heat energy supplied = Change in internal energy / Heat energy supplied
For an ideal diatomic gas, the change in internal energy when heated at constant pressure is given by:
∆U = (5/2) n R ∆T
Where n is the number of moles of gas, R is the gas constant, and ∆T is the change in temperature.
The heat energy supplied to the gas is given by:
Q = n Cp ∆T
Where Cp is the specific heat capacity of the gas at constant pressure.
Therefore, the fraction of heat energy supplied which increases the internal energy of the gas is:
Fraction of heat energy supplied = (∆U / Q) = [(5/2) n R ∆T] / [n Cp ∆T]
Simplifying the equation, we get:
Fraction of heat energy supplied = (5/2) R / Cp
For an ideal diatomic gas, Cp = (7/2) R /n. Substituting this in the above equation, we get:
Fraction of heat energy supplied = 5/7
Hence, the correct answer is option D, 5/7.
Fraction of heat energy supplied = Change in internal energy / Heat energy supplied
For an ideal diatomic gas, the change in internal energy when heated at constant pressure is given by:
∆U = (5/2) n R ∆T
Where n is the number of moles of gas, R is the gas constant, and ∆T is the change in temperature.
The heat energy supplied to the gas is given by:
Q = n Cp ∆T
Where Cp is the specific heat capacity of the gas at constant pressure.
Therefore, the fraction of heat energy supplied which increases the internal energy of the gas is:
Fraction of heat energy supplied = (∆U / Q) = [(5/2) n R ∆T] / [n Cp ∆T]
Simplifying the equation, we get:
Fraction of heat energy supplied = (5/2) R / Cp
For an ideal diatomic gas, Cp = (7/2) R /n. Substituting this in the above equation, we get:
Fraction of heat energy supplied = 5/7
Hence, the correct answer is option D, 5/7.
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When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas, isa)2/5b)3/5c)3/7d)5/7Correct answer is option 'D'. Can you explain this answer?
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