Question

How much heat energy must be added to a 6.0-cm-diameter copper sphere to raise its temperature from -50∘C to 170 ∘C?

The correct answer is Q=85kJ, but I do not know how to solve.

Answer 1

First we will determine the mass of the copper.

Diameter of copper sphere = 6.0 cm = 0.06 m

So, radius, r = 0.06/2 = 0.03 m

Hence, volume of copper sphere, V = (4/3)*pi*r^3 = (4/3)*3.141*0.03^3 = 0.00011308 m^3

Density of copper = 8940 kg/m^3

Hence, mass of the copper, m = V x density = 0.00011308 x 8940 = 1.0109 kg.

Initial temperature, T1 = -50 deg C

Final temperature, T2 = 170 deg C

So,

quantity of heat energy required to raise the temperature of copper,

Q = m*s*(T2 - T1)

where, s = specific heat capacity = 376.81 J/(kg-K)

So,

Q = 1.0109*376.81*(170+50)

= 83801 J

= 83.8 kJ (Answer)

Your answer is 85 kJ, this may be due to taking some approximation during calculations.