A heart defibrillator passes 10.0 A through a patient’s torso for 5.00 ms in an attempt to restore normal beating. Find the temperature increase caused in the 8.00 kg of affected tissue if all the energy heats up the tissue with a specific heat capacity of 3000 J kg-1 K-1.
To find the temperature increase caused in the affected tissue, we can use the equation:
ΔQ = mcΔT
where:
ΔQ is the change in thermal energy,
m is the mass of the affected tissue,
c is the specific heat capacity of the tissue, and
ΔT is the change in temperature.
First, let's calculate the change in thermal energy (ΔQ).
We know that current (I) is equal to the rate of flow of charge (Q) per unit time (t):
I = Q / t
Rearranging the formula, we can solve for Q:
Q = I * t
Substituting the given values:
Q = (10.0 A) * (5.00 ms) = 50.0 C
Now, we can calculate the change in temperature (ΔT).
Using the formula:
ΔT = ΔQ / (m * c)
Substituting the given values:
ΔT = 50.0 C / (8.00 kg * 3000 J kg^(-1) K^(-1))
Calculating:
ΔT = 50.0 C / 24000 J K^(-1)
Simplifying:
ΔT = 0.00208 K
Therefore, the temperature increase caused in the 8.00 kg of affected tissue is approximately 0.00208 K.