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Chapter 9: Problem 1322

The molar specific heat at constant pressure for a monoatomic gas is (A) \((3 / 2) \mathrm{R}\) (B) \((5 / 2) \mathrm{R}\) (C) \(4 \mathrm{R}\) (D) \((7 / 2) \mathrm{R}\)

Short Answer

Expert verified
The molar specific heat at constant pressure (Cp) for a monoatomic gas is (B) \(\frac{5}{2} R\).

Step by step solution

01

Understanding equipartition theorem

The equipartition theorem states that each degree of freedom in a system contributes \(\frac{1}{2} k T\), where \(k\) is Boltzmann's constant and \(T\) is temperature, to the total internal energy. For a monoatomic gas, there are only 3 translational degrees of freedom (corresponding to the movement along the x, y, and z axis).
02

Express Cp in terms of R

We know that the molar specific heat at constant volume (Cv) for a monoatomic gas can be expressed as: Cv = (Degree of freedom / 2) *R Here, R is the molar gas constant, and degree of freedom is 3 for a monoatomic gas. Now we can find the specific heat at constant pressure: Cp = Cv + R
03

Calculate Cp for the monoatomic gas

Now, substitute the values in the equation and calculate Cp: Cp = (3/2) * R + R
04

Simplify the expression for Cp

Simplify the expression for Cp: Cp = (5/2) * R So, for a monoatomic gas, the molar specific heat at constant pressure is: Cp = (5/2) * R From the options given in the exercise, the correct choice is: (B) (5/2) * R

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Most popular questions from this chapter

At what temperature the molecules of nitrogen will have the same rms. velocity as the molecules of Oxygen at \(127^{\circ} \mathrm{C}\). (A) \(273^{\circ} \mathrm{C}\) (B) \(350^{\circ} \mathrm{C}\) (C) \(77^{\circ} \mathrm{C}\) (D) \(457^{\circ} \mathrm{C}\)

Air is filled in a bottle at atmospheric pressure and it is corked at \(35^{\circ} \mathrm{C}\), If the cork can come out at 3 atmospheric pressure then upto what temperature should the bottle be heated in order to remove the cork. (A) \(325.5^{\circ} \mathrm{C}\) (B) \(651^{\circ} \mathrm{C}\) (C) \(851^{\circ} \mathrm{C}\) (D) None of these

A perfect gas at \(27^{\circ} \mathrm{C}\) is heated at constant pressure to \(327^{\circ} \mathrm{C}\). If original volume of gas at \(27^{\circ} \mathrm{C}\) is \(\mathrm{V}\) then volume at \(327^{\circ} \mathrm{C}\) is (A) \(2 \mathrm{~V}\) (B) \(\mathrm{V}\) (C) (V/2) (D) \(3 \mathrm{~V}\)

A sample of gas is at \(0^{\circ} \mathrm{C}\). To what temperature it must be raised in order to double the rms speed of molecule. (A) \(270^{\circ} \mathrm{C}\) (B) \(819^{\circ} \mathrm{C}\) (C) \(100^{\circ} \mathrm{C}\) (D) \(1090^{\circ} \mathrm{C}\)

The volume of a gas at pressure \(21 \times 10^{4} \mathrm{Nm}^{-2}\) and temperature \(27^{\circ} \mathrm{C}\) is 83 Liters. If $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. Then the quantity of gas in \(\mathrm{g}\) -mole will be (A) 42 (B) 7 (C) 14 (D) 15
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