First slide

Thermodynamic processes

Question

20 grams of a gas occupies 100 cc volume at pressure $10^{5}$ dyne/ $c m^{2}$ . If during isothermal process the pressure is changed to $10^{4}$ dyne/ $c m^{2}$ , the volume of the gas in cc will be:

Moderate

A

10
B

50
C

200
D

1000

Solution

$\begin{array}{rcl} g a s e q u a t i o n i n i s o t h e r m a l p r o c e s s i s P V & = & c o n s \tan t \\ P_{1} V_{1} {=P}_{2} V_{2} \\ h e r e i n i t i a l p r e s s u r e o f g a s, P_{1} & = & 10^{5} d y n e c m^{- 2}, F i n a l p r e s s u r e o f g a s, {P_{2}}_{} = 10^{4} d y n e c m^{- 2} \\ V_{1} {=100cc,V}_{2} i n i t i a l, f i n a l v o l u m e o f g a s \\ s u b s t i t u t e t h e v a l u e s i n a b o v e g a s e q u a t i o n \\ {⇒10}^{5} {×100=10}^{4} \times V_{2} \\ \Rightarrow & V_{2} = 1000 cc is final volume of gas \end{array}$

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