A diatomic gas does 80J of work when expands isobarically Find the heat given to the gas during this process?

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Solution

Given
Work done in isobaric (constant pressure) process, W = 80 J
$\Rightarrow W = P ∆ V = 80 J F r o m i d e a l g a s e q u a t i o n a t c o n s \tan t p r e s s u r e w e h a v e P ∆ V = n R ∆ T \Rightarrow ∆ T = \frac{P ∆ V}{n R} = \frac{80 J}{n R} - - - (1)$
$A l s o C h a n g e i n i n t e r n a l e n e r g y d u r i n g t h e p r o c e s s i s g i v e n b y ∆ U = n C_{v} ∆ T = n \frac{R}{γ - 1} ∆ T F o r d i a t o m i c g a s, γ = 7 / 5 P u t t i n g t h e v a l u e o f ∆ T f r o m E q . (1) w e g e t ∆ U = \frac{n R}{\frac{7}{5} - 1} \frac{80 J}{n R} = \frac{5}{2} \times 80 J = 200 J$

$F r o m 1 s t l a w o f t h e r m o d y n a m i c s H e a t g i v e n t o g a s i s g i v e n b y ∆ Q = ∆ U + W \Rightarrow ∆ Q = 200 J + 80 J = 280 J A n s w e r$

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