A cup of coffee (with lid) is enclosed in an insulated cup 0.5 cm thick in the shape of a cube 9.7 cm on a side. The thermal conductivity of the cup is 0.0002 cal/s x cm x C. The temperature of the coffee is 71 degrees Celsius and the temperature of the surroundings is 25 degrees Celsius. Find the heat loss due to conduction in J/s.
I did it like this:
[0.0002 (6x9.7^2)(71-25)]/0.5 = 10.388
but it was wrong.
Where did you convert calories to Joules?
it's true but ur answer is in cal you need to multiply it by 4.18 to convert it to joul
Yes your answer is right and you need to multiply 4.18 to get the final correct answer
To calculate the heat loss due to conduction, we need to use the formula for conduction:
Q = k * A * (T1-T2) / d
where:
Q is the heat loss in Joules per second (J/s)
k is the thermal conductivity of the cup material, given as 0.0002 cal/s x cm x °C
A is the surface area of the cup in square centimeters (cm^2)
T1 is the temperature of the coffee, given as 71 °C
T2 is the temperature of the surroundings, given as 25 °C
d is the thickness of the cup, given as 0.5 cm
Now, let's calculate the surface area of the cup:
A = 6 * (side length)^2
= 6 * (9.7 cm)^2
= 6 * (94.09 cm^2)
= 564.54 cm^2
Now, we can substitute the values into the formula:
Q = (0.0002 cal/s x cm x °C) * (564.54 cm^2) * (71 °C - 25 °C) / (0.5 cm)
To convert from calories to Joules, we can divide by the conversion factor of 4.184 J/cal:
Q = (0.0002 cal/s x cm x °C) * (564.54 cm^2) * (71 °C - 25 °C) / (0.5 cm) * (4.184 J/cal)
= (564.54 cm^2) * (46 °C) / (0.5 cm) * (0.0002 cal/s x cm x °C) * (4.184 J/cal)
= (11722.84 cm^3 x °C) / (0.5 cm) * (0.0002 cal/s x °C) * (4.184 J/cal)
= (11722.84 cm^3 x °C) * (0.0002 cal/s) * (4.184 J/cal) / (0.5 cm)
= 488.85 J/s
Therefore, the heat loss due to conduction is approximately 488.85 J/s.