Question

What is the specific heat of the metal?
cal/g•°C

Answer 1

I don't have the numbers from your experiment — to find the metal's specific heat you need the masses and temperatures. Give those and I can compute it. Meanwhile, here is the formula and how to use it.

Basic idea (no heat lost to surroundings):
heat lost by metal = heat gained by water (+ calorimeter, if present)

If no calorimeter:
m_m c_m (T_m,i − T_f) = m_w c_w (T_f − T_w,i)

Solve for the metal's specific heat c_m:
c_m = [m_w c_w (T_f − T_w,i)] / [m_m (T_m,i − T_f)]

Where
- m_m = mass of metal (g)
- m_w = mass of water (g)
- T_m,i = initial metal temperature (°C)
- T_w,i = initial water temperature (°C)
- T_f = final (equilibrium) temperature (°C)
- c_w = 1.00 cal/g·°C (water)
- c_m will be in cal/g·°C

If your calorimeter has heat capacity C_cal (in cal/°C), include it on the RHS:
c_m = [m_w c_w (T_f − T_w,i) + C_cal (T_f − T_cal,i)] / [m_m (T_m,i − T_f)]

Example:
m_m = 25.0 g, T_m,i = 95.0 °C
m_w = 50.0 g, T_w,i = 22.0 °C
T_f = 28.0 °C
c_m = [50·1·(28 − 22)] / [25·(95 − 28)] = 300 / 1675 = 0.179 cal/g·°C

Typical specific heats (for reference, cal/g·°C):
- Aluminum ≈ 0.215
- Copper ≈ 0.092
- Iron ≈ 0.111
- Lead ≈ 0.031
- Silver ≈ 0.056
- Gold ≈ 0.0305

Post the masses and temperatures (and calorimeter heat capacity if used) and I'll compute the metal's specific heat for you.