Thermodynamics and Entropy- reservoir and block problem

[emmy]

Homework Statement

A 382 g block is put in contact with a thermal reservoir. The block is initially at a lower temperature than the reservoir. Assume that the consequent transfer of energy as heat from the reservoir to the block is reversible. Figure 20-22 gives the change in entropy ΔS of the block until thermal equilibrium is reached. The scale of the horizontal axis is set by Ta = 280 K and Tb = 520 K. What is the specific heat of the block?

Homework Equations

ΔS= mC_spln(T/T_o)

The Attempt at a Solution

ΔS= mC_spln(T/T_o)

C_sp=ΔS/(m*ln(T/T_o))

where
ΔS= 100 J/K
m= .382 kg
T=520K
T_o=280K

plug and chug,
C_sp= 100/(.382*ln(520/280)) =422.88J/K*kg

where did I go wrong ):

 

[quietrain]

your T₀ is not T_a

look carefully at the graph^^

 

[emmy]

your T₀ is not T_a

look carefully at the graph^^

Ohhhhh my gosh this is why i miss points on exams lol! Thanks c: