Specific Heat Capacity ( Chem Grads and\or Professors ) Please !!!?

Question

Okay I don't understand what we have to do here. I mean like theres so many given numbers ... and i've looked in my text book and theres so many equations i dont know which one to pick... If anyone can please help me. You don't need to give me the anwser, if you like change the numbers around that would be okay ( as long as they make sense ) but yeah.. i would really appreciate it if someone can show me step by step.

Thanks sooooo much.

A 25.5-g sample of an unknown metal is heated to 92.5°C and is placed in a perfectly insulated container along with 184.g of water at an initial temperature of 20.05°C. After a short time the temperature of both the metal and water become equal at 23.30°C.
The specific Heat Capacity of water is 4.18 J/g/K in this temperature range.
What is the specific heat capacity of the metal?

Answer 1

The heat loss of the metal is equal to the heat gain of the liquid.

The heat gain of the water is 184 g x (23.30-20.05) deg C x 4.18 J/g deg C = 2499.64 J [Note: deg K and deg C are equivalent here]

The heat loss of the metal is 25.5g x (92.5-23.30) deg C x Sp. Heat Capacity = 2499.64 J
Sp. Heat Capacity = 1.417 J / g deg C

Answer 2

There are two concepts here: Heat capacity, and specific heat. They are different. Let's get started. Heat capacity has units of cal/g-degC. Specific heat is a ratio with no units.

Let the sample be called S. The heat lost by the sample is equal to the heat gained by the water.

92.5C - 23.20C = 69.30degC decrease by the sample
23.20C - 20.05C = 3.15degC increase by the water

184gH2O x 3.15degC x 4.18J/g-C = 2423 J heat lost by the water and gained by the metal.

2423J /25.5gS/69.3C = 1.37 J/g-C

Answer 3

IF m_metal is mass of the metal, T2 is the final temperature the metal and water equalise at, Cp denotes heat capacity, T1 the starting temperature of each substance etc:

m_metal.Cp_metal.(T2 - t1_metal) = m_water.Cp_water.(T2-T1_water)

Rearranging for Cp_metal:
Cp_metal = m_water.Cp_water.(T2-T1_water)/[m_metal.(T2 - T1_metal)]

But your textbook should already have told you all this, right? ;)