Question 9.2: Heating a 24.0-g aluminum can raises its temperature by 15.0......
Heating a 24.0-g aluminum can raises its temperature by 15.0°C. Find the value of q for the can.
Strategy Heat flow depends on the heat capacity of the material being heated, the size of the sample, and the change in temperature. Because the information given is in mass, it will be easiest to use the specific heat rather than the molar heat capacity. The value of the specific heat of aluminum can be found in Table 9.2.
| Table 9.2 | ||
| Specific heat and molar heat capacities for some common substances | ||
| Substance | Specific Heat, c ( J g^{–1} K^{–1}) |
Molar Heat Capacity, C_p ( J mol^{–1} K^{–1}) |
| Al(s) | 0.900 | 24.3 |
| Cu(s) | 0.385 | 24.5 |
| H_2O(s) | 2.09 | 37.7 |
| H_2O(ℓ) | 4.18 | 75.3 |
| H_2O(g) | 2.03 | 36.4 |
q = mcΔT
=24.0\ g\times{\frac{0.900\,{\mathrm{J}}}{{\mathrm{g}}{\ }^{\circ}{\mathrm{C}}}}\times15.0^{\circ}{\mathrm{C}}
= 324 J
Analyze Your Answer It may take some practice to gain a feel for the correct magnitude for heat. We do know that q should have energy units, and the units in our calculation are consistent with that. We can also look at the order of magnitude for the quantities involved to make sure our arithmetic makes sense. The mass and the temperature change are both on the order of 10¹, whereas the specific heat is on the order of 10^0, or 1. So the product of the three should be on the order of 10², and an answer in hundreds of joules makes sense.
Check Your Understanding A block of iron weighing 207. g absorbs 1.50 kJ of heat. What is the change in the temperature of the iron?