Question

Two bars of identical mass are at 27 °C. One is made from glass and the other from another substance. The specific heat capacity of glass is 840 J/(kg · C°). When identical amounts of heat are supplied to each, the glass bar reaches a temperature of 93 °C, while the other bar reaches 258.0 °C. What is the specific heat capacity of the other substance?

Answer 1

Here, we will us the equation Q = m c delta T, to solve the problem.

In the above expression -

Q is heat, m mass, c specific heat and delta T the change in temperature

writing in terms of c, we have

c = Q/(m c delta T)

In the above, we see that the the change in temp varies inversely with the specific heat

so if the glass reaches 93 C, its delta T is 93 - 27 = 66, and delta T for the other bar is 258 - 27 = 231

This is 231/66 = 3.50 times greater than the delta T for glass

therefore, the specific heat for the other bar must be 1/4.30 times the specific heat for glass,

So, specific heat capacity of the other substance = (840 J/kg/C) / 3.5 = 240.0 J/kg/C.