The expression for internal energy in terms of pressure and volume of an ideal m

Question

The expression for internal energy in terms of pressure and volume of an ideal monatomic gas is:

a. 0.5 PV

b. PV

c. 1.5 PV

d. 2 PV

e. None of the above

At a constant temperature T, which of the following will be true about the kinetic energy and the velocity of two types of ideal molecules with different masses?

a. The kinetic energy will be the same but the larger mass molecules will have a smaller velocity.

b. The kinetic energy will be the same but the larger mass molecules will have a larger velocity.

c. The kinetic energy of the larger mass molecule will be larger but its velecity will be smaller.

d. The kinetic energy of the larger mass molecule will be larger and its velecity will be larger.

e. The kinetic energy of the larger mass molecule will be smaller and its velecity will be smaller.

Explanation / Answer

Internal energy of ideal monotomic gas, U = Qv = nCvT = n(1.5R)T = 1.5nRT = 1.5PV

Hence, correct option is (c)

KE of ideal molecule = 1.5kT

KE depends only on temperature.

RMS speed of ideal molecule = (3kT/m)1/2

where m = molecular mass. Hence, velocity is larger for molecule of smaller molecular mass.

Hence, correct option is (a)

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