First slide

Heat ;work and internal energy

Question

When an ideal diatomic gas is heated at constant pressure, the fraction of heat energy supplied which increases the internal energy of the gas is:

Moderate

A

$\frac{2}{5}$
B

$\frac{3}{5}$
C

$\frac{3}{7}$
D

$\frac{5}{7}$

Solution

$\begin{array}{rcl} a m o u n t o f h e a t a b s o r b e d b y g a s a t c o n s \tan t p r e s s u r e i s \\ {dQ=nC}_{p} dT \\ i n c r e a s e i n i n t e r n a l e n e r g y o f g a s i s \\ {dU=nC}_{v} dT \\ h e r e m i s m a s s o f g a s, \\ C i s m o l a r s p e c i f i c h e a t o f g a s, \\ d T i s c h a n g e i n t e m p e r a t u r e \\ ∴ f r a c t i o n o f h e a t e n e r g y s u p p l i e d w h i c h i n c r e a s e s t h e i n t e r n a l e n e r g y o f t h e g a s i s \frac{dU}{dQ} & = & \frac{C_{v}}{C_{p}} \\ \frac{dU}{dQ} & = & \frac{5R/2}{7R/2} s u b s t i t u t i n g v a l u e s f o r a d i a t o m i c g a s \\ \frac{dU}{dQ} = \frac{5}{7} . \end{array}$

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