Question

A sample of an ideal gas is taken through the cyclic process $ABCA$ shown in figure. It rejects $50J$ of heat during the part $AB$, does not absorb or reject the heat during $BC$, and accepts $70J$ of heat during $CA$. 40 joules of work is done on the gas during the part $BC$. The internal energies at $B$ and $C$, respectively, will be (Internal Energy at A=1500Joules)

• A. $1450J$ and $1410J$
• B. $1550J$ and $1590J$
• C. $1450J$ and $1490J$
• D. $1550J$ and $1510J$

Answer 1

The correct option is C $1450J$ and $1490J$

$A\to B$ is an ischoric process

$\Delta W=0,\Delta U=\Delta Q,\Delta U=-50J$

$U_A-U_b=50\Rightarrow 1500-V_B=50V_B=1450J$

Along $BC,\Delta Q=0$

$\Delta W=-\Delta U$

$\Delta U=+40J$

In $V_C-V_B=40J$

$V_C=V_B+70V_C=1450+40=1490J$

$1450J$ and $1490J$