When a gas expands along AB, it does 500J of work and absorbs 250 J of heat. When the gas expands along AC, it does 700J of work and absorbs 300J of heat.

(a) How much heat does the gas exchange along Bc?
(b) When the gas makes the transition from C to A along CDA, 800J of work are done on it from C to D. How much heat does it exchange along CDA?

Answer

A, B, D

Explanation

(a) `U_C-U_A` along two paths should be same.
`:.` `(Q_(AB)+Q_(BC))-(W_(AB)+W_(BC))=Q_(AC)-W_(AC)`
`:.` `(250+Q_(BC))-(500+0)=300-700`
Solving, we get
`Q_(BC)=-150J`
(b) `Q_(CDA)=(W_(CD)+W_(DA))+(U_(A)_U_(C))`
`=(-800+0)-(U_C-U_A)`
`=-800-(300-700)`
`=-400J`