Suppose a block of lead of mass 0.4kg at temperature of 95°C is dropped in 2kg of water originally at 20°C in a container. Calculate the final temprereture if no heat is lost to the container and enviroment ;(specific heat of lead is 128j/kg°C and water ;4184j/kg°C
Confused so want answer to that question please help me out??
I'm not really sure of the process of working out so kindly seeking your help
gdsss
To calculate the final temperature of the system, we need to use the principle of conservation of energy. The energy lost by the lead block will be gained by the water.
First, let's calculate the energy lost by the lead block:
Q_lead = mass_lead * specific_heat_lead * change_in_temperature_lead
= 0.4 kg * 128 J/kg°C * (T_final - 95°C)
Here, T_final is the final temperature of the entire system.
Next, let's calculate the energy gained by the water:
Q_water = mass_water * specific_heat_water * change_in_temperature_water
= 2 kg * 4184 J/kg°C * (T_final - 20°C)
Since no heat is lost to the container and environment, the energy lost by the lead block (Q_lead) is equal to the energy gained by the water (Q_water):
Q_lead = Q_water
0.4 kg * 128 J/kg°C * (T_final - 95°C) = 2 kg * 4184 J/kg°C * (T_final - 20°C)
Now, let's solve this equation for T_final:
0.4 * 128 * (T_final - 95) = 2 * 4184 * (T_final - 20)
51.2 * (T_final - 95) = 8368 * (T_final - 20)
51.2 * T_final - 51.2 * 95 = 8368 * T_final - 8368 * 20
51.2 * T_final - 4864 = 8368 * T_final - 167360
8368 * T_final - 51.2 * T_final = 167360 - 4864
8316.8 * T_final - 51.2 * T_final = 162496
8265.6 * T_final = 162496
T_final = 162496 / 8265.6
T_final ≈ 19.66°C
Therefore, the final temperature of the system will be approximately 19.66°C.