A 150 g sample of metal at 55.0 C raises the temperature of 150 g of water from 23.0 C to 35.0 C. Determine the specific heat of the metal in J/g C.
Hint: #1 First find heat absorbed by water using formula q = mass x specific heat x change in temp (of water).
#2 Use this value to solve for specific heat of the metal. Remember final temperatures is the same for both metal and water.
Specific heat of water is 4.184 J/g C
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heat lost by the metal + heat gained by the water = 0.
mass metal x specific heat metal x [(Tfinal-Tinital)] + [mass water x specific heat water x (Tfinal-Tinital)] = 0
To determine the specific heat of the metal in J/g C, we can follow these steps:
Step 1: Calculate the heat absorbed by water using the formula q = mass x specific heat x change in temperature.
Given:
- Mass of water = 150 g
- Change in temperature of water = (35.0 C - 23.0 C) = 12.0 C
- Specific heat of water = 4.184 J/g C
Using the formula, we have:
q_water = (150 g) x (4.184 J/g C) x (12.0 C)
q_water = 7536.96 J
Step 2: Use the value of the heat absorbed by water to solve for the specific heat of the metal.
Since the final temperature for both the metal and water is the same, we can assume that the heat absorbed by the metal is equal to the heat released by the water. Therefore, the heat absorbed by the metal can be expressed as:
q_metal = -q_water (negative sign indicates heat released)
Substituting the value of q_water, we have:
q_metal = -7536.96 J
Step 3: Calculate the specific heat of the metal.
The specific heat (C) is defined as the heat (q) absorbed by a substance divided by its mass (m) and the change in temperature (ΔT).
Specific heat of the metal (C_metal) = q_metal / (mass of metal x change in temperature of the metal)
Given:
- Mass of metal = 150 g
- Change in temperature of the metal = (35.0 C - 23.0 C) = 12.0 C
Using the formula, we have:
C_metal = (-7536.96 J) / (150 g x 12.0 C)
C_metal ≈ -4.16 J/g C
Note: The negative sign in the value of the specific heat of the metal signifies that the metal is releasing heat.
So, the specific heat of the metal is approximately -4.16 J/g C.