In thermodynamics, we are interested in the magnitude of the heat flow when a process takes place. The quantity of heat flow is designated q, and its sign is determined by the direction of heat flow.

The computation of q for a process where the system only changes temperature is simple. q depends on the change in temperature (DT = T_final - T_initial) and the heat capacity, C of the system. The heat capacity is the amount of heat required to raise the temperature of the system by 1^oC and is usually given in units of J/^oC. q is just the product of C and DT, q = C*DT

The heat capacity itself depends on the amount of substance in the system and the specific heat of that substance. C = mc, where c is the specific heat. The specific heat is the amount of heat required to raise the temperature of 1 gram of the substance by 1^oC and is usually given in units of J/g^oC.

Combining the two relationships, we find that q = m*c*DT

Example:

Gaseous carbon dioxide has a specific heat of 0.843 J/g^oC. What is the value of q if a 5.0 gram sample of CO₂(g) is warmed from 25.0 to 30.0^oC?

Solution: Use the above relationship for q, q = m*c*DT
m = 5.0 grams
c = 0.843 J/g^oC
DT = T_final - T_initial = (30.0-25.0) = 5.0 ^oC

q = 5.0 g * 0.843 J/g^oC * 5.0 ^oC = 21 J.

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