# A sample of an ideal gas is taken through the process ABCA shown . It rejects 50 J of heat during part AB , does not absorb or reflect heat during BC and accepts 70 J of heat during CA . Forty joules of work is done on the gas during the part BC . The internal energies at B and C respectively will be $\;(u_{A} =1500\;J)$

$(a)\;1450\;J\;and\;1410\;J\qquad(b)\;1550\;J\;and\;1590\;J\qquad(c)\;1450\;J\;and\;1490\;J\qquad(d)\;1550\;J\;and\;1510\;J$

Answer : $\;1450\;J\;and\;1490\;J$
Explanation :
$A \to B \;$ is an isochoric process
$\bigtriangleup W=0\;, \bigtriangleup u = \bigtriangleup Q \;, \bigtriangleup u = -50\;J$
$V_{A} - V_{B} =50$
$1500 - V_{B} = 50$
$V_{B} = 1450 \;J$
along BC , $\;\bigtriangleup Q =0$
$\bigtriangleup W = - \bigtriangleup u$
$\bigtriangleup u= + 40\; J$
in $\;V_{C} -V_{B} = 40 \;J$
$V_{C} = V_{B} +70$
$V_{C} = 1450 + 40 =1490\;J$