First slide

Heat ;work and internal energy

Question

140 calories of heat is required to raise the temperature of 2 moles of an ideal diatomic gas at constant pressure from 0° C to 10°C. How much heat is required to heat it through same range at constant volume?

Moderate

A

60 calories
B

100 calories
C

180 calories
D

140 calories

Solution

$a m o u n t o f h e a t r e q u i r e d t o r a i s e t e m p e r a t u r e o f g a s a t c o n s \tan t p r e s s u r e i s g i v e n b y$
${(d Q)}_{p} = n C_{p} d T$
${(d Q)}_{p} = 140 c a l o r i e s (g i v e n)$
$n = n u m b e r o f m o l e s = 2 (g i v e n)$
$C_{p} = s p e c i f i c h e a t a t c o n s \tan t p r e s s u r e$
$d T = c h a n g e i n t e m p e r a t u r e = 10 - 0 = 10^{0} C$
$s u b s t i t u t e g i v e n v a l u e s i n t h e a b o v e f o r m u l a$
$140 = 2 C_{p} (10)$
$\Rightarrow C_{p} = 7$
$γ = \frac{C_{p}}{C_{v}} = 1.4 (g i v e n)$
$s u b s t i t u t e C_{p} v a l u e i n a b o v e e q u a t i o n, w e g e t C_{v} = 5$
$a m o u n t o f h e a t r e q u i r e d t o r a i s e t e m p e r a t u r e o f g a s a t c o n s \tan t v o l u m e i s g i v e n b y$
${(d Q)}_{v} = n C_{v} d T = 2 (5) 10 = 100 c a l o r i e$

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