Answer
$Q = 4500 J$
Work Step by Step
From the figure, we find the gradient of the graph by using Pythagoras Theorem.
$(400-200)^2 + (20 -15) ^2 = m^2$
$ m = -40$
Find the y-intercept, C of the straight line equation
$y = -40x +C$
At the point $ (5, 400)$ we can find the y-intercept
$ 400 = (-40)(5) +C$
$ C = 600$
From here, find the final temperature, $T_f$ at point $(20, y)$
$y = -40(20) +600$
$y = -800 + 600$
$y = 200$
So the final temperature is $ 200K$
Next, we can find the absorbed energy from the equation
$ Q = (\frac{T_i + T_f}{2})(\Delta S)$
$ Q = (\frac{400 K+ 200K}{2})(20J/K-5J/K)$
$Q = 4500 J$
