4.0 g of a gas occupies 22.4 L at NTP. The specific heat capacity of the gas at constant volume is 5.0 JK^-1 mol^-1. If the speed of sound in this gas at NTP is 952 ms^-1, then the heat capacity at constant pressure is.
(Take gas constant R = 8.3 Jk^-1 mol^-1)

8.0 JK^-1mol^-1

7.5 JK^-1mol^-1

7.0 JK^-1mol^-1

8.5 JK^-1mol^-1

Solution

8.0 JK^-1mol^-1

Given, M = 4 gm
V= 22.4 L,
C_V = 5 JK^-1 mol^-1
_{$straight v subscript sound space equals 952 space straight m divided by straight s comma straight C subscript straight p space equals ? As comma space velocity space of space sound comma space straight v subscript sound space equals space square root of γpV over straight M end root rightwards double arrow space straight gamma space equals space straight M over pV straight V subscript sound superscript 2 space equals space straight C subscript straight p over straight C subscript straight v so comma space heat space capacity space at space constant space pressure comma straight C subscript straight p space equals space straight C subscript straight v open square brackets straight M over pV close square brackets straight v subscript sound superscript 2 space equals space 5 space open square brackets fraction numerator 4 space straight x space 10 to the power of negative 3 end exponent over denominator 10 to the power of 5 space straight x space 22.4 space straight x space 10 to the power of negative 3 end exponent end fraction close square brackets left parenthesis 952 right parenthesis squared equals fraction numerator 20 over denominator 22.4 end fraction space straight x space left parenthesis 952 right parenthesis squared space straight x space 10 to the power of negative 5 end exponent equals space 809.200 space straight x space 10 to the power of negative 5 end exponent space equals space 8.09 space straight j divided by mol space straight K.$}

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Some More Questions From Mechanical Properties of Fluids Chapter

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