First slide

Thermodynamic processes

Question

A mono atomic ideal gas initially at $17^{o} C$ is suddenly compressed to one-eighth of its original volume. The temperature after compression is

Moderate

A

$16^{o} c$
B

$17^{o} c$
C

$887^{o} c$
D

$n o n e$

Solution

$\begin{array}{rcl} s u d d e n p r o c e s s i s a d i a b a t i c p r o c e s s \\ I n a d i a b a t i c p r o c e s s r e l a t i o n b e t w e e n t e m p e r a t u r e T, V o l u m e V i s \\ {TV}^{γ-1} =constant \\ h e r e s p e c i f i c h e a t r a t i o i s {γ=5/3 for monoatomic gas,T}_{1} =17°C=17+273=290K (∵ C = K - 273) \\ \Rightarrow & T_{1} {V_{1}}^{γ-1} = T_{2} {V_{2}}^{γ-1} \\ \Rightarrow & \frac{T_{1}}{T_{2}} = {(\frac{V_{2}}{V_{1}})}^{γ-1} \\ \Rightarrow & \frac{290}{T_{2}} = {(\frac{1}{8})}^{\frac{5}{3} -1} \\ \Rightarrow & \frac{290}{T_{2}} = {(\frac{1}{8})}^{\frac{2}{3}} \\ \Rightarrow & \frac{290}{T_{2}} = {(\frac{1}{2})}^{2} \\ \Rightarrow & T_{2} {=1160 K⇒T}_{2} =1160-273=887°C \\ \Rightarrow & T_{2} {=887}^{o} c \end{array}$

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