Question 4.19: Calculating Specific Heat We heat 50.0 g of an unknown subst...
Calculating Specific Heat
We heat 50.0 g of an unknown substance by adding 205 cal, and its temperature rises by 7.0°C. What is its specific heat? Using Table 4.2, identify the substance.
| Table 4.2 Specific Heats for Some Common Substances | |||
| Specific Heat (cal/g · °C) | Substance | Specific Heat (cal/g · °C) | Substance |
| 0.42 | Wood (typical) | 1.00 | Water |
| 0.22 | Glass (typical) | 0.48 | Ice |
| 0.20 | Rock (typical) | 0.48 | Steam |
| 0.59 | Ethanol | 0.11 | Iron |
| 0.61 | Methanol | 0.22 | Aluminum |
| 0.56 | Ether | 0.092 | Copper |
| 0.21 | Carbon tetrachloride | 0.031 | Lead |
Strategy
We solve the equation for specific heat by substituting the values for mass, amount of heat, and temperature change. We compare the number we obtain with the values in Table 4.2 to identify the substance.
The substance in Table 4.2 having a specific heat of 0.59 cal/g·°C is ethanol.
Is this answer reasonable? If we had water with SH = 1 cal/g·°C, instead of an unknown substance raising the temperature of 50.0 g by 7.0°C would require 50 \times 7.0 = 350\ \text{cal}. But we added only approximately 200 cal. Therefore, the SH of the unknown substance must be less than 1.0. How much less? Approximately 200/350 = 0.6. The actual answer, 0.59 cal/g·°C, is quite reasonable.
■ Quick Check 4.19
It required 88.2 cal to heat 13.4 g of an unknown substance from 23°C to 176°C. What is the specific heat of the unknown substance? Check your answer to see whether it is reasonable.