Kinetic Theory Of Gases Question 11
Question: Carbon monoxide is carried around a closed cyclic process $ abc $ , in which be is an isothermal process, as shown in figure. The gas absorbs 7000 J of heat as its temperature is increased from 300 K to 1000 K in going from a to b. The quantity of heat ejected by the gas during the process ca is
Options:
A) 4200 J
B) 500 J
C) 9000J
D) 9800J
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ Q _{ab}=+7000=\mu C _{v}(1000-300) $ …(i)
For the process ca: $ T _{a}=300K, $
$ T _{c}=T _{b}=1000K $
$ Q _{Ca}=\mu C _{P}(300-1000)=-\mu C _{p}\times 700 $
$ =-\mu (C _{v}+R)700 $ …(ii)
For carbon monoxide: $ T _{a}=300K, $
$ T _{c}=T _{h}=1000K $
$ {(\Delta Q) _{ca}}$
=$\mu C _{p}(300-1000)=-\mu C _{P}\times 700 $
$ =-\mu (C _{v}+R)700 $
For carbon monoxide: $ \gamma =\frac{7}{5} $
$ C _{v}=\frac{R}{\gamma -1}=\frac{R}{\frac{7}{5}-1}=\frac{5R}{2} $ …(iii)
Hence, form Eq. (i) $ 7000=\mu \frac{5R}{2}\times 700 $ Or $ \mu R=\frac{20}{5}=4 $
$ Q _{ca}=-(7000+4\times 700)=-9800J $ Negative sing shows that heat is ejected.
BETA
