Tongue touches a pipe . Calculate final temperature of the tongue. 500 g of aluminum. ambient temp is -5 degrees Celsius. tongue is 100 g. heat capacity is same as pure water. assume heat capacity of aluminum is 24 J/molK.
You have to assume there is no blood supply (adding heat) to the tongue.
massAL*24J/molK*(Tf+5)=massT*Cwater(Tf-37)
To calculate the final temperature of the tongue after touching a pipe, we need to use the principle of heat transfer and the concept of heat capacity.
The initial step is to find the heat transferred from the tongue to the aluminum pipe. The equation for heat transfer is:
Q = mcΔT
Where:
Q is the heat transferred (in joules),
m is the mass (in grams),
c is the specific heat capacity (in J/g°C), and
ΔT is the change in temperature (in °C).
Given data:
m (mass of the tongue) = 100 g
c (specific heat capacity of water) = the same as pure water = 4.18 J/g°C
ΔT (change in temperature) = final temperature of the tongue – initial temperature of the tongue
The heat transferred from the tongue to the aluminum pipe is the same as the heat absorbed by the aluminum pipe. Therefore, we can use the same equation again to solve for ΔT with the following data:
m (mass of the aluminum pipe) = 500 g
c (specific heat capacity of aluminum) = 24 J/molK (we will convert it to J/g°C later)
ΔT (change in temperature) = final temperature of the aluminum – initial temperature of the aluminum
We know that the heat transferred between the tongue and the pipe results in an equal change in temperature for both.
Based on this information, we can set up the following equation:
(mass of the tongue) × (specific heat capacity of water) × ΔT (tongue) = (mass of the aluminum pipe) × (specific heat capacity of aluminum) × ΔT (aluminum)
Substituting the given values, we have:
(100 g) × (4.18 J/g°C) × ΔT (tongue) = (500 g) × (24 J/g°C) × ΔT (aluminum)
Now we need to calculate the specific heat capacity of aluminum in J/g°C. To do this, we divide the given value by the molar mass of aluminum, which is 26.98 g/mol:
(24 J/molK) / (26.98 g/mol) = 0.889 J/g°C
Substituting this value back into our equation, we have:
(100 g) × (4.18 J/g°C) × ΔT (tongue) = (500 g) × (0.889 J/g°C) × ΔT (aluminum)
Simplifying the equation further:
418 ΔT (tongue) = 500 ΔT (aluminum)
Next, rearrange the equation to solve for ΔT (aluminum):
ΔT (aluminum) = (418 ΔT (tongue)) / 500
Since we know the initial temperature of the tongue is the ambient temperature (-5°C), we can calculate the final temperature of the tongue (T (tongue, final)) by adding ΔT (tongue) to the initial temperature of the tongue:
T (tongue, final) = -5°C + ΔT (tongue)
Finally, we substitute the values to find the final temperature of the tongue:
T (tongue, final) = -5°C + [(418 ΔT (tongue)) / 500]