When 1 liter of ice at a temperature of -18°C comes into contact with 1 liter of water at a temperature of 16°C, heat will flow between the two substances until they reach a common final temperature. To determine the final temperature, we can use the principle of energy conservation, assuming no heat loss to the surroundings:
The heat gained by the ice = the heat lost by the water.
The heat gained or lost by a substance can be calculated using the formula:
Q = m * c * ΔT
where: Q is the heat gained or lost (in joules), m is the mass of the substance (in kilograms), c is the specific heat capacity of the substance (in J/kg·K), ΔT is the change in temperature (in Kelvin).
Given: Mass of ice = 1 liter = 1 kg Initial temperature of ice = -18°C = 255 K Specific heat capacity of ice = 2090 J/kg·K
Mass of water = 1 liter = 1 kg Initial temperature of water = 16°C = 289 K Specific heat capacity of water = 4184 J/kg·K
To find the final temperature, we equate the heat gained and lost:
(m_ice * c_ice * ΔT_ice) = (m_water * c_water * ΔT_water)
(1 kg * 2090 J/kg·K * (T_f - 255 K)) = (1 kg * 4184 J/kg·K * (T_f - 289 K))
Simplifying the equation:
2090 * (T_f - 255) = 4184 * (T_f - 289)
2090T_f - 2090 * 255 = 4184T_f - 4184 * 289
2090T_f - 534450 = 4184T_f - 1208276
2090T_f - 4184T_f = -1208276 + 534450
-2094T_f = -673826
T_f = (-673826) / (-2094)
T_f ≈ 322.18 K
The final temperature of the mixture of ice and water after 1 second of contact is approximately 322.18 Kelvin (or about 49.03 degrees Celsius).