In one cycle, a heat engine absorbs $1\mathrm{.}68$ kJ from a hot reservoir at $277$C and expels $1\mathrm{.}24$ kJ to a cold reservoir at $27$C$.$

$($a$)$

What is the engine's thermal efficiency $($in percent$)?$

$\%$

$($b$)$

How much work is done by the engine $($in J$)$ in each cycle?

J

$($c$)$

What is the engine's power output $($in kW$)$ if each cycle lasts $0\mathrm{.}301$ s$?$

kW

PA $=1\mathrm{.}01106$ Pa$,$

PB $=5\mathrm{.}10105$ Pa$,$

and

PC $=2\mathrm{.}02105$ Pa$.$

$($a$)$ Find the volumes VA and VB$.$

VA$=$ m$3$VB$=$ m$3$

$($b$)$ Find the work done in each process of the cycle and the total work done for the whole cycle.

WAB$=$ JWBC$=$ JWCD$=$ JWDA$=$ JWtot$=$ J

$($c$)$ Find the change in thermal energy during the constant$-$volume process BC$.$

J