1. Calculate the amount of heat necessary to raise the temperature of a 3 kg sample of aluminum from 40°C to 95°C if the specific heat capacity is 900 J/kg°C.
2. Copper has a specific heat capacity of 385 J/kg°C. What is the temperature change of a 4.1 kg sample of copper when 780 J of energy is applied?
To calculate the amount of heat necessary to raise the temperature of a sample of a material, you can use the formula:
Q = mcΔT
where:
Q is the amount of heat (in Joules),
m is the mass of the sample (in kilograms),
c is the specific heat capacity of the material (in J/kg°C), and
ΔT is the change in temperature (in °C).
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1. For the first question, you have:
m = 3 kg (mass of aluminum sample)
c = 900 J/kg°C (specific heat capacity of aluminum)
ΔT = 95°C - 40°C = 55°C (change in temperature)
Plugging these values into the formula, we get:
Q = (3 kg)(900 J/kg°C)(55°C)
Q = 148,500 J
So, the amount of heat necessary to raise the temperature of the aluminum sample from 40°C to 95°C is 148,500 Joules.
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2. For the second question, you have:
m = 4.1 kg (mass of copper sample)
c = 385 J/kg°C (specific heat capacity of copper)
Q = 780 J (amount of heat applied)
Since we are given the amount of heat applied, we can rearrange the formula to solve for ΔT:
ΔT = Q / (mc)
ΔT = 780 J / (4.1 kg)(385 J/kg°C)
ΔT ≈ 0.491°C
So, the temperature change of the copper sample when 780 J of energy is applied is approximately 0.491°C.