How do you determine the specific heat of a material if a 35 g sample absorbed 96 J as it was heated from 293 to 313 K?

Question

Naomi Aronson · Accepted Answer

#"specific heat" = 0.137 J/(g^oC)#

Specific heat capacity of a substance is the amount of heat required to raise one gram of the substance by one degree Celsius. This means the first thing you need to do is convert your temperatures to Celsius.

#""^@C = K - 273.15#

#T_1 = 293 - 273.15 = 19.85 ^@ C#

#T_2 = 313 - 273.15 = 39.85 ^@ C#

#Delta T = T_2 - T_1 = 20.00 ^@ C#

#"specific heat" = q/(m xx Delta T)#,

where #q = "heat in Joules", " "m = "mass in grams"#

#"specific heat" = 96/(35 xx 20.00) = 0.137 J/(g^oC)#

Cameron Andrews · Answer

undefined To determine the specific heat ($C$) of a material, you can use the formula:

$$ Q = m \cdot C \cdot \Delta T $$

where:
- $ Q $ is the heat absorbed (in joules),
- $ m $ is the mass of the material (in grams),
- $ C $ is the specific heat of the material (in J/g·K),
- $ \Delta T $ is the change in temperature (in Kelvin).

Rearrange the formula to solve for $ C $:

$$ C = \frac{Q}{m \cdot \Delta T} $$

Substitute the given values:

$$ C = \frac{96 \, \text{J}}{35 \, \text{g} \cdot (313 \, \text{K} - 293 \, \text{K})} $$

$$ C \approx \frac{96 \, \text{J}}{35 \, \text{g} \cdot 20 \, \text{K}} $$

$$ C \approx \frac{96 \, \text{J}}{700 \, \text{g} \cdot \text{K}} $$

$$ C \approx 0.137 \, \text{J/g} \cdot \text{K} $$

Therefore, the specific heat of the material is approximately $0.137 \, \text{J/g} \cdot \text{K}$.