First slide

Heat ;work and internal energy

Question

For the same raise in temperature of two moles of gas at constant pressure, the heat required for triatomic gas is K times the heat required for monoatomic gas. The value of K is

Moderate

A

$\frac{3}{2}$
B

$\frac{5}{2}$
C

$\frac{8}{3}$
D

$\frac{8}{5}$

Solution

molar specific heat of gas at constant pressure for tri atomic gas (6° of freedom)
$C_{p} =4R$

$m o l a r s p e c i f i c h e a t o f g a s a t c o n s \tan t p r e s s u r e i s C_{p} C_{p} = \frac{5}{2} R for monoatomic gas$
$h e a t r e q u i r e d f o r r a i s e i n t e m p e r a t u r e o f g a s a t c o n s \tan t p r e s s u r e i s Q = n C_{p} ∆T$
$Q_{t r i a t o m i c} = k Q_{m o n o t o m i c} s u b s t i t u t e t h e v a l u e s$
$n (4 R) ∆T=kn(\frac{5 R}{2}) ∆ T$

$∴ K= \frac{4R}{\frac{5}{2} R} = \frac{8}{5}$
Heat required is $\frac{8}{5}$ times.

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