Question

The stone block has a mass of 592.6g and a specific heat capacity of 1200J/Kg°C. A heater supplies 200W of heat energy for 5 minutes. What would the increase in temperature be?

Answer 1

The quantity of heat needed to produce the increase in temperature of the stone block can be found from the formula:

$$Q=mc\Delta T,$$

here, $Q$ is the quantity of heat needed to produce the increase in temperature, $\Delta T$, of the stone block; $m=0.5926\ kg$ is the mass of the stone block; c=1200\ \dfrac{J}{kg\cdot\! ^{\circ}C} is the specific heat capacity of the stone block.

The quantity of heat supplied by a heater in time $t$ can be found from the formula:

$$Q=Pt,$$

here, $P$ is the power of the heater.

Finally, we can equate these two expressions and calculate $\Delta T$:

$$Pt=mc\Delta T,$$ $$\Delta T=\dfrac{Pt}{mc},$$ \Delta T=\dfrac{200\ W\cdot 5\ min \dfrac{60\ s}{1\ min}}{0.5926\ kg\cdot 1200\ \dfrac{J}{kg\cdot\! ^{\circ}C}}=84.4\ ^{\circ}C.

Answer:

$\Delta T=84.4\ ^{\circ}C.$