The value of specific heat at constant volume is 0.723 kJ/kgK, if the density of gas at 27°C and $10^{5} {Nm}^{-2}$ is $1.2 {kg m}^{- 3}$ , what is the specific heat at constant pressure?

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0.8 k J/kg K

1 k J/kg K

0.9 k J/kg K

1.2 k J/kg K

answer is A.

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Detailed Solution

$\begin{array}{rcl} a s s p e c i f i c h e a t a t c o n s \tan t v o l u m e & = & c_{v} = 0.723 k i l o j o u l e / k g K i s g i v e n \\ m a s s o f g a s i s c o n s i d e r e d, u n i t d o e s n o t h a s n u m b e r o f m o l e s o f g a s \\ h e n c e g a s e q u a t i o n t h a t n e e d t o b e c o n s i d e r e d i s P V & = & m r T \\ \Rightarrow & r = \frac{P V}{m T} - - - (1) \\ P r e s s u r e i s P & = & 10^{5} N m^{- 2} \\ d e n s i t y & = & \frac{m a s s (m)}{v o l u m e (v)} = 1.2 K g m^{- 3} \\ T e m p e r a t u r e & = & 27 + 273 k e l v i n = 300 K \\ s u b s t i t u t e a b o v e g i v e n v a l u e s i n e q u a t i o n (1) \\ r & = & \frac{P V}{m T} = \frac{10^{5}}{1.2 x 300} = 0.2777 k i l o j o u l e k g^{- 1} K^{- 1} \\ f r o m d i f f e r e n c e o f s p e c i f i c h e a t s \\ c_{p} & = & c_{v} + r - - - (2) \\ g i v e n c_{v} & = & 0.723 k i l o j o u l e / k g K \\ r & = & 0.2777 k i l o j o u l e k g^{- 1} K^{- 1} \\ s u b s t i t u t e a b o v e v a l u e s i n (2) e q u a t i o n \\ c_{p} & = & 0.723 + 0.2777 = 1.007 k J k g^{- 1} K^{- 1} \end{array}$