Answer:
c_m = 0.4814 J/g°C
Step-by-step explanation:
From thermo equilibrium conditions, we now that;
Heat lost by the Metal = Heat gained by the Water
Thus;
-Q_m = Q_w
Q_m = m_m × c_m × Δt_m
Also,
Q_w = m_w × c_w × Δt_w
We are given;
Mass of metal; m_m = 10 kg
Initial temperature of the metal; t_mi = 50°C
Change in temperature of metal; Δt_m = (31.4 - 50) = -18.6 °C
Mass of water; m_w = 1 kg
Initial temperature of the water; t_wi = 10°C
Change in temperature of water; Δt_w = 31.4°C - 10°C = 21.4 °C
Specific heat capacity of water; c_w = 4.184 J/g°C
We are looking for c_m which is the specific heat capacity of the metal.
Now, from -Q_m = Q_w;
-(m_m × c_m × Δt_m) = (m_w × c_w × Δt_w)
Let's make c_m the subject;
c_m = (m_w × c_w × Δt_w)/(-m_m × Δt_m)
Plugging in the relevant values;
c_m = (1 × 4.184 × 21.4)/(-10 × -18.6)
c_m = 0.4814 J/g°C