How much heat is required to raise an 850g copper pan from 18C to 85C if
(a) the pan is empty?
(b) the pan contains 1.9kg of water?
(c) the pan contains 4.3kg of mercury?
To determine the amount of heat required to raise the temperature of an object, you can use the heat capacity (also known as specific heat) formula:
Q = mcΔT
where:
Q is the amount of heat energy required (in joules),
m is the mass of the substance (in kilograms),
c is the specific heat capacity of the substance (in joules per kilogram per degree Celsius), and
ΔT is the change in temperature (in degrees Celsius).
For copper, the specific heat capacity is approximately 0.385 J/g°C or 385 J/kg°C.
(a) For an empty copper pan:
m = 850g = 0.85kg
ΔT = (85°C - 18°C) = 67°C
Using the formula:
Q = mcΔT
Q = (0.85kg) * (385 J/kg°C) * (67°C)
Q ≈ 22382.25 Joules
So, approximately 22,382.25 Joules of heat are required to raise the temperature of an 850g copper pan from 18°C to 85°C when it is empty.
(b) For a copper pan containing 1.9kg of water:
m = 1.9kg
ΔT = (85°C - 18°C) = 67°C
Using the formula:
Q = mcΔT
Q = (1.9kg) * (4186 J/kg°C) * (67°C)
Q ≈ 550,909.4 Joules
So, approximately 550,909.4 Joules of heat are required to raise the temperature of an 850g copper pan containing 1.9kg of water from 18°C to 85°C.
(c) For a copper pan containing 4.3kg of mercury:
m = 4.3kg
ΔT = (85°C - 18°C) = 67°C
Using the formula:
Q = mcΔT
Q = (4.3kg) * (139 J/kg°C) * (67°C)
Q ≈ 31,600.3 Joules
So, approximately 31,600.3 Joules of heat are required to raise the temperature of an 850g copper pan containing 4.3kg of mercury from 18°C to 85°C.