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26. (AIEEE 2007 )

If C p and C v denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

(A) C p C v = 28 R

(B) C p C v = R / 28

(C) C p C v = R / 14

(D) C p C v = R

Correct answer is (B)

According to Mayer's relationship C p C v = R
C p M C v M = R M Here M = 28.

27. (AIEEE 2005 )

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio C p C v of the mixture is

(A) 1.62

(B) 1.59

(C) 1.54

(D) 1.4

Correct answer is (A)

n 1 + n 2 r 1 = n 1 r 1 1 + n 2 r 2 1
16 4 + 16 32 r 1 = 16 / 4 5 3 1 + 16 / 32 1.4 1
γ = 1.62

28. (AIEEE 2004 )

One mole of ideal monatomic gas ( γ = 5 / 3 ) is mixed with one mole of diatomic gas ( γ = 7 / 5 ) . What is γ for the mixture? γ Denotes the ratio of specific heat at constant pressure, to that at constant volume

(A) 35 / 23

(B) 23 / 15

(C) 3 / 2

(D) 4 / 3

Correct answer is (C)

n 1 + n 2 γ 1 = n 1 γ 1 1 + n 2 γ 2 1
1 + 1 γ 1
= 1 5 3 1 + 1 7 5 1
γ = 3 2

29. (AIEEE 2002 )

1 mole of a gas with γ = 7 / 5 is mixed with 1 mole of a gas with γ = 5 / 3 , then the value of γ for the resulting mixture is

(A) 7 / 5

(B) 2 / 5

(C) 3 / 2

(D) 12 / 7

Correct answer is (C)

If n 1 moles of adiabatic exponent γ 1 is mixed with n 2 moles of adiabatic exponent γ 2 then the adiabatic component of the resulting mixture is given by

n 1 + n 2 γ 1 = n 1 γ 1 1 + n 2 γ 2 1
1 + 1 γ 1 = 1 7 5 1 + 1 5 3 1

2 γ 1 = 5 2 + 3 2 = 4

2 = 4 γ 4 γ = 6 4 = 3 2