The specific heat of solid copper is 0.385 J/g*C. What thermal energy change occurs when the temperature of a 40.10g sample of copper is cooled from 42.9C to 10.0C? Be sure to give you answer the proper sign.
I know this is part of the answer which
(42.9-10.0)*40.10*0.385=508 the second of the answer is where I am confused on
This is amount of heat is used to melt solid ice at 0.0C. The molar heat of fusion of ice is 6.00 kJ/mol. How many moles of ice are melted?
To calculate the thermal energy change for cooling solid copper, you can use the formula:
Q = m * c * ΔT
Where:
Q is the thermal energy change
m is the mass of the sample in grams (40.10g in this case)
c is the specific heat capacity of copper (0.385 J/g*C in this case)
ΔT is the change in temperature (42.9C - 10.0C = 32.9C in this case)
Plugging in the values:
Q = 40.10g * 0.385 J/g*C * 32.9C = 508 J (since g and C cancel out in the units)
Now for the proper sign:
The sample of copper is being cooled, which means it is losing thermal energy. In physics conventions, losing thermal energy is considered negative. Therefore, the sign for the answer should be negative:
Q = -508 J
Moving on to the second question:
To determine the number of moles of ice melted, we can use the equation:
Q = n * ΔH
Where:
Q is the amount of heat required to melt the ice
n is the number of moles of ice
ΔH is the molar heat of fusion of ice (6.00 kJ/mol in this case)
First, we need to convert the molar heat of fusion from kilojoules to joules:
ΔH = 6.00 kJ/mol * 1000 J/kJ = 6000 J/mol
Plugging in the values:
-508 J = n * 6000 J/mol
To solve for n, you can rearrange the equation:
n = -508 J / 6000 J/mol
n ≈ -0.085 mol
Since we can't have a negative number of moles, we can disregard the negative sign. Therefore, approximately 0.085 moles of ice are melted.