If 20g of water at 60 degree centigrade is mixed with 60g of water at 20 degree centigrade the resultant temperature is
the sum of heats gained is zero.
20*c*(Tf-60)+60c(Tf-20)=0
solve for Tf
30℃
To find the resultant temperature when two substances at different temperatures are mixed, we can use the principle of energy conservation. The total heat lost by one substance equals the total heat gained by the other substance.
In this case, we have two substances: water at 60°C and water at 20°C.
First, let's calculate the heat lost or gained by each substance.
The heat lost by the water at 60°C can be calculated using the formula:
Q = m * c * ΔT
Where:
Q is the heat lost (or gained),
m is the mass of the substance,
c is the specific heat capacity of the substance,
ΔT is the change in temperature.
The specific heat capacity of water is approximately 4.18 J/g°C.
For the water at 60°C:
Q1 = 20g * 4.18 J/g°C * (60°C - T)
Q1 = 83.6 J/g°C * (60°C - T)
The heat gained by the water at 20°C can be calculated using the same formula:
Q2 = 60g * 4.18 J/g°C * (T - 20°C)
Q2 = 250.8 J/g°C * (T - 20°C)
Since energy is conserved, the heat lost by one substance should be equal to the heat gained by the other substance:
Q1 = Q2
83.6 J/g°C * (60°C - T) = 250.8 J/g°C * (T - 20°C)
Next, we can solve this equation to find the value of T, which is the resultant temperature.
83.6 J/g°C * 60°C - 83.6 J/g°C * T = 250.8 J/g°C * T - 250.8 J/g°C * 20°C
5001.6 J - 83.6 J/g°C * T = 250.8 J/g°C * T - 5016 J
83.6 J/g°C * T + 250.8 J/g°C * T = 5016 J - 5001.6 J
334.4 J/g°C * T = 14.4 J
T = 14.4 J / 334.4 J/g°C
T ≈ 0.043 °C
Therefore, the resultant temperature when 20g of water at 60°C is mixed with 60g of water at 20°C is approximately 0.043°C.