A 50g sample of metal was heated to 100 degrees Celsius and then dropped into a beaker containing 50g of water at 25 degrees Celsius. If the specific heat of the metal is .25 cal/g degrees Celsius, what is the final temperature of the water?

A. 27
B. 40
C. 60
D. 86
(units are degrees Celsius)

I don't know how to go about solving this. Help please?

Thank you

heat lost by metal + heat gained by water = 0

[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat water x (Tfinal-Tinitial)] = 0
Substitute and solve for Tfinal, the only unknown.

Sample of gas is heated from 25c to 55c it will expand by

wecrwtvey

To solve this problem, we can use the principle of conservation of energy. The heat gained by the water is equal to the heat lost by the metal.

First, let's calculate the heat lost by the metal:
Heat lost = (mass of the metal) x (specific heat of the metal) x (change in temperature of the metal)
Heat lost = 50g x 0.25 cal/g°C x (100°C - final temperature of the metal)

Next, let's calculate the heat gained by the water:
Heat gained = (mass of the water) x (specific heat of water) x (change in temperature of the water)
Heat gained = 50g x 1 cal/g°C x (final temperature of the water - 25°C)

Since the heat lost by the metal is equal to the heat gained by the water, we can set up an equation:
Heat lost = Heat gained

50g x 0.25 cal/g°C x (100°C - final temperature of the metal) = 50g x 1 cal/g°C x (final temperature of the water - 25°C)

Now we can solve for the final temperature of the water:

12.5(100 - final temperature of the metal) = final temperature of the water - 25

1250 - 12.5(final temperature of the metal) = final temperature of the water - 25

12.5(final temperature of the metal) + final temperature of the water = 1275

Now we have an equation with two unknowns, so we need another equation to solve the system. Since the final temperature of the water is the same as the final temperature of the metal (since they are mixed), we can make the following substitution:

final temperature of the water = final temperature of the metal

Therefore, our equation becomes:

25(final temperature of the metal) + final temperature of the metal = 1275

Simplifying:

26(final temperature of the metal) = 1275

(final temperature of the metal) = 1275 / 26

(final temperature of the metal) ≈ 49.04°C

Since the final temperature of the water is the same as the final temperature of the metal, we can conclude that the final temperature of the water is approximately 49.04°C.

Therefore, the closest option from the given answer choices is:

D. 86

However, please note that the exact value would be slightly different, so the correct answer may not be exactly 86 degrees Celsius.