An insulated beaker contains 250.0 grams of water at 25C. Exactly 41.6 g of a metal at 100.0C was dropped in the beaker. The final temperature of the water was 26.4C. Assuming that no heat is lost in any other way, calculate the specific heat of the metal.

heat lost by hot metal + heat gained by cooler water = 0

[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat water x (Tfinal-Tinitial)] = 0
Solve for specific heat metal. You have all of the other items.

did not help

answer choices:
a. 0.159 J g-1 K-1
b. 0.478 J g-1 K-1
c. 0.0503 J g-1 K-1
d. 2.09 J g-1 K-1

Read my response at your later post. You missed something.

[41.6xmx1.5]+[18x4.186x1.5]=0

6.24m+113.022=0
62.4m=-113.022
m=113.022/62.4
m=1.81125
not an answer choice?

To calculate the specific heat of the metal, we can use the principle of conservation of heat. The heat gained by the water should be equal to the heat lost by the metal.

The formula to calculate heat energy is:

Q = mcΔT

Where:
Q = heat energy (in Joules)
m = mass of the substance (in grams)
c = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)

Given:
Mass of water (m1) = 250.0 g
Initial temperature of water (T1) = 25.0 °C
Mass of metal (m2) = 41.6 g
Initial temperature of metal (T2) = 100.0 °C
Final temperature of the water (T3) = 26.4 °C

First, we calculate the heat gained by the water:
Q1 = m1 * c1 * ΔT1

Substituting the values:
Q1 = (250.0 g) * c1 * (26.4 °C - 25.0 °C)

Next, we calculate the heat lost by the metal:
Q2 = m2 * c2 * ΔT2

Substituting the values:
Q2 = (41.6 g) * c2 * (26.4 °C - 100.0 °C)

Since the heat gained by the water is equal to the heat lost by the metal (assuming no heat lost to the surroundings), we can set Q1 equal to Q2 and solve for the specific heat of the metal (c2):

(250.0 g) * c1 * (26.4 °C - 25.0 °C) = (41.6 g) * c2 * (26.4 °C - 100.0 °C)

Simplifying the equation, we can solve for c2:

c2 = [(250.0 g) * c1 * (26.4 °C - 25.0 °C)] / [(41.6 g) * (26.4 °C - 100.0 °C)]

Now you can plug in the value of the specific heat capacity of water (c1 = 4.18 J/g°C) and calculate the specific heat of the metal (c2).