The amount of energy needed to heat 2.00 g of carbon from 50.0°C to 80.0°C is 42.6 J. The specific heat capacity of this sample of carbon is ?

Question

Caleb Adams · Accepted Answer

Carbon has a specific heat of 0.710 J/g * C. With the information at your disposal, you can calculate the specific heat of carbon by using #q = m * c * DeltaT#, where #q# - the amount of heat needed - in your case 42.6 J;
#m# - the mass of the sample - in your case 2.00 g;
#c# - the specific heat of carbon;
#DeltaT# - the difference between the final and the initial temperature - in your case #80^@"C"# and #50^@"C"#; Enter all of the data into the equation now. #q = m * c * DeltaT => c = q/(m * DeltaT)# #c = "42.6 J"/("2.00 g" * (80.0-50.0)^@"C") = 0.710 "J"/("g" * ^@"C")#

Wyatt Atkins · Answer

undefined To find the specific heat capacity of carbon, use the formula:

$ q = mcΔT $

Where:
- $ q $ is the amount of heat energy (42.6 J in this case)
- $ m $ is the mass of the substance (2.00 g)
- $ c $ is the specific heat capacity (what we're trying to find)
- $ ΔT $ is the change in temperature (80.0°C - 50.0°C = 30.0°C)

Rearranging the formula to solve for $ c $:

$ c = \frac{q}{mΔT} $

Plug in the values:

$ c = \frac{42.6 \, \text{J}}{2.00 \, \text{g} \times 30.0 \, \text{°C}} $

$ c = \frac{42.6 \, \text{J}}{60.0 \, \text{g} \cdot \text{°C}} $

$ c = 0.71 \, \text{J/g°C} $