First slide

Heat ;work and internal energy

Question

The value of $γ$ for helium is 5/3. Calculate the specific heat capacity at constant volume, if it’s molar mass is 4:

Moderate

A

5187.5 J/kg K
B

3112.5 J/kg K
C

31.125 J/kg K
D

3.1125 J/kg K

Solution

we know that $C_{V}$ =3R/2=12.45 J/ mol-K for helium which is monoatomic. Therefore, specific heat capacity of gas at constant volume is
$c_{v} = \frac{C_{v}}{M} = \frac{12.45}{4} {=3.1125 Jgm}^{- 1} K^{- 1}$
$C_{v} =molar specific heat of gas at constant volume$
$M = m o l e c u l a r w e i g h t$
Or $c_{v} = 3.1125 \times 10^{3} {Jkg}^{- 1} K^{- 1}$
$\Rightarrow c_{v} = 3112.5 {Jkg}^{- 1} K^{- 1}$

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