Answer:
90.64 degrees
Explanation:
Lets list out the parameters given in the question.
Mass of Cup = 270g
Temp. of cup = 94.1C
Specific heat capacity of C = 4.18J/gC
Temp. of Silver spoon = 26.8C
heat capacity of the silver spoon = 61.2 J/C
The fact that thermal equilibrium was mentioned simply means that;
Heat Lost by coffee= Heat gained by spoon
The relationship between the parameters mentioned is given as;
Q = m* c * dT
Where;
m is the mass, c is the specific heat capacity and dT is the "change" in temperature.
Assume the final temperature of the whole system is "x". They would both have the same final temperature since they are in thermal equilibrium.
Heat lost by coffee = 270 * 4.18 * (94.1 - x)
(94.1 -x) because coffee will loose heat, hence temperature of coffee will fall.
Heat gained by spoon = c *dT = 61.2 * (x - 26.8).
dT = Final Temp. - Initial Temp.
dT = x - 26.8
Heat lost = Heat gained :
270 * 4.18 * (94.1 - x) = 61.2 * (x - 26.8),
1128.6 (94.1 - x) = 61.2 (x- 26.8)
18.44 ( 94.1 - x) = x - 26.8
1735.2 - 18.44 x = x - 26.8
1735.2 + 26.8 = x + 18.44 x
1762 = 19.44 x
x = 90.64 degrees
