Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs her hands back and forth for a total of 12 rubs a distance of 7.50 cm each and with a frictional force averaging 30.0 N, what is the temperature increase? The mass of tissue warmed is only 0.100 kg, mostly in the palms and fingers.
This is my answer:
Delta T=(30N*18*0.075m)/(0.100kg*3500J/kg.C)
To calculate the temperature increase, we can use the equation:
Q = m * c * ΔT
Where:
Q = Heat energy (Joules)
m = Mass of tissue warmed (kg)
c = Specific heat capacity of the tissue (J/kg*K)
ΔT = Change in temperature (K)
First, let's calculate the work done by the frictional force:
Work (W) = Force (F) * Distance (d)
W = 30.0 N * 12 * 7.5 cm
Note that we need to convert the distance to meters:
W = 30.0 N * 12 * 0.075 m
Next, let's calculate the heat energy (Q) produced:
Q = W
Since all the work is converted to heat energy:
ΔT = Q / (m * c)
Now, we need to find the specific heat capacity (c) of the tissue. This value represents how much energy is required to raise the temperature of the tissue by 1 Kelvin (or Degree Celsius):
The specific heat capacity of human tissue is approximately 1,800 J/kg*K.
Now, let's substitute the values into the equation:
ΔT = Q / (m * c)
ΔT = (30.0 N * 12 * 0.075 m) / (0.100 kg * 1800 J/kg*K)
Calculate the numerator:
ΔT = (30.0 * 12 * 0.075) / (0.100 * 1800)
Calculate the denominator:
ΔT = (30.0 * 12 * 0.075) / 180
Calculate the numerator:
ΔT = 0.225 / 180
ΔT = 0.00125
Therefore, the temperature increase is approximately 0.00125 Kelvin.
To determine the temperature increase, we need to calculate the amount of work done by the frictional force and then convert it to thermal energy. The formula for work is given by:
Work = Force x Distance
First, let's calculate the total work done:
Work = Frictional force x Total distance
Total distance = Number of rubs x Distance per rub
Total distance = 12 rubs x 7.50 cm
Now, convert the distance to meters:
Total distance = (12 rubs x 7.50 cm) / 100 cm/m
Next, substitute the given values:
Total distance = (12 x 7.50 cm) / 100 cm/m
Total distance = 0.90 m
Substituting this value into the equation for work:
Work = 30.0 N x 0.90 m
Work = 27 J
Since energy is conserved, this work is converted into thermal energy. We can now determine the temperature increase using the specific heat formula:
Q = mcΔT
Where:
Q = Thermal energy (in Joules)
m = Mass (in kg)
c = Specific heat capacity (in J/kg°C)
ΔT = Temperature change (in °C)
Given:
m = 0.100 kg
c = Specific heat capacity (we need to look this up)
Q = 27 J
ΔT = ?
To determine the specific heat capacity, we need to look it up for the tissue (in this case, mostly in the palms and fingers). Each material has its own specific heat capacity value.
Once we have the specific heat capacity, we can rearrange the equation to solve for ΔT:
ΔT = Q / (mc)
Substituting the known values:
ΔT = 27 J / (0.100 kg x c)
Now, you would need to look up the specific heat capacity of the tissue. Once you have that value, plug it into the equation to calculate the temperature increase.
heat=force*distance=30*12*.075 Joules
heat=mass*specificheat*DeltaTemp
now for the specific heat of skin, it is mostly water, so I would use the specific heat of water for that. Solve for delta Temp