First slide

Heat ;work and internal energy

Question

For a certain gas the ratio of specific heat is 1.5, for this has:

Moderate

A

$C_{p} = \frac{5R}{J}$
B

$C_{v} = \frac{3R}{J}$
C

$C_{v} = \frac{5R}{J}$
D

$C_{p} = \frac{3R}{J}$

Solution

$\begin{array}{rcl} specific heat ratio = γ= \frac{C_{p}}{C_{v}} =1.5 \\ {⇒ C}_{p} {=1.5C}_{v} \\ d i f f e r e n c e o f s p e c i f i c h e a t s i s C_{p} - C_{v} & = & \frac{R}{J} \\ s u b s t i t u t e g i v e n v a l u e s i n a b o v e e q u a t i o n \\ {and C}_{p} - \frac{C_{p}}{1.5} = \frac{R}{J} \\ {or C}_{p} & = & \frac{R}{J (1 - \frac{1}{1.5})} = \frac{3R}{J} . \end{array}$

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