If the temperatures of separate 34 g samples of gold, mercury, and carbon are to be raised by 10.0°C. How much heat must be applied to each substance?
To calculate the amount of heat required for each substance, we will use the equation:
q = mcΔT
where,
q is the heat (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in J/g°C),
ΔT is the change in temperature.
First, we need to determine the specific heat capacity (c) for each substance.
The specific heat capacities for gold, mercury, and carbon are as follows:
- Gold: 0.129 J/g°C
- Mercury: 0.14 J/g°C
- Carbon: 0.711 J/g°C
Next, we calculate the heat required for each substance:
For gold:
- Mass (m) = 34 g
- Specific heat capacity (c) = 0.129 J/g°C
- Change in temperature (ΔT) = 10.0°C
Using the formula:
q = mcΔT
q = (34 g) * (0.129 J/g°C) * (10.0°C)
q = 44.034 J
Therefore, 44.034 Joules of heat must be applied to the 34 g sample of gold.
For mercury:
- Mass (m) = 34 g
- Specific heat capacity (c) = 0.14 J/g°C
- Change in temperature (ΔT) = 10.0°C
Using the formula:
q = mcΔT
q = (34 g) * (0.14 J/g°C) * (10.0°C)
q = 47.88 J
Therefore, 47.88 Joules of heat must be applied to the 34 g sample of mercury.
For carbon:
- Mass (m) = 34 g
- Specific heat capacity (c) = 0.711 J/g°C
- Change in temperature (ΔT) = 10.0°C
Using the formula:
q = mcΔT
q = (34 g) * (0.711 J/g°C) * (10.0°C)
q = 242.94 J
Therefore, 242.94 Joules of heat must be applied to the 34 g sample of carbon.
In summary:
- Gold requires 44.034 Joules of heat.
- Mercury requires 47.88 Joules of heat.
- Carbon requires 242.94 Joules of heat.