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I have a doubt, kindly clarify. 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 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

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 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-l)

  • Option 1)

    7.5 JK-1 mol-1

  • Option 2)

    7.0 JK-1 mol-1

  • Option 3)

    8.5 JK-1 mol-1

  • Option 4)

    8.0 JK-1 mol-1

 
Answers (1)
932 Views
V Vakul

As we learnt

Atomicity or adiabatic coefficient (gamma) -

gamma =frac{ C_{p}}{ C_{v}}

=1+frac{2}{f}

 

- wherein

for Monoatomic gas     gamma= frac{5}{3}

for Diatomic gas         gamma= frac{7}{5}

for Triatomic gas        gamma= frac{4}{3}

 

 

given  M=4gm

V=22. 4L

C_{v}=5.0JK^{-1}mol^{-1}

V_{sound}=952m/s

C_{p}=?

Velocity of sound

V_{sound}=\sqrt{\frac{rpv}{M}}

or\: r=\frac{MV^{2}_{sound}}{PV}

\frac{(952)^{2}\times 4\times 10^{-3}}{10^{5}\times 22.4\times 10^{-3}}

\because r=\frac{C_{p}}{C_{v}}

=> C_{p}=rc_{v}

=\frac{(952)^{2}\times 4\times 10^{-3}\times5}{10^{5}\times 22.4\times 10^{-3}}

=> C_{p}=8.09J/mol-k


Option 1)

7.5 JK-1 mol-1

Option is incorrect

Option 2)

7.0 JK-1 mol-1

Option is incorrect

Option 3)

8.5 JK-1 mol-1

Option is incorrect

Option 4)

8.0 JK-1 mol-1

Option is correct

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