Question 448: Waves

Question

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K
$$-$$1
mol
$$-$$1
. If the speed of sound in this gas at NTP  is 952 m s
$$-$$1
, then the heat capacity at constant pressure is
(Take gas constant R $$=$$ 8.3 J K
$$-$$1
mol
$$-$$1
)

Accepted Answer

Molar mass of the gas = 4g/mol
Speed of sound
$$V = \sqrt {{{\gamma RT} \over m}}  \Rightarrow 952 = \sqrt {{{\gamma  	imes 3.3 	imes 273} \over {4 	imes {{10}^{ - 3}}}}} $$
$$ \Rightarrow \gamma  = 1.6 = {{16} \over {10}} = {8 \over 5}$$
Also, $$\gamma  = {{{C_P}} \over {{C_V}}} = {8 \over 5}$$
$$ \Rightarrow {C_P} = {{8 	imes 5} \over 5} = 8\,J{K^{ - 1}}mo{l^{ - 1}}$$
[C
V
= 5.0 JK
Ã¢ÂÂ1
given]

Answer

7.0 J K
$$-$$1
mol
$$-$$1

Answer

8.5 J K
$$-$$1
mol
$$-$$1

Answer

8.0 J K
$$-$$1
mol
$$-$$1

Answer

7.5 J K
$$-$$1
mol
$$-$$1

Waves

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K $-1 mol -1 . If the speed of sound in this gas at NTP is 952 m s -1 , then the heat capacity at constant pressure is (Take gas constant R = 8.3 J K -1 mol -$1 )

Choose the correct answer: