THERMODYNAMICS - First law of thermodynamics, conservation of energy, internal energy

First law of thermodynamics

- conservation of energy

- energy can be transformed or changed from one form to another

- energy can neither be created nor destroyed

- the increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings


dU = dQ - dW


dU = dQ - PdV


dU = TdS - PdV



where:

dQ = TdS

dW = PdV

dU = change in the internal energy of the system

dQ = heat added to the system

dW = work done by the system


sign convention of dQ and dW

(-) dQ < 0 if energy is lost from the system as heat

(+) dW > 0 if energy is lost from the system as work



1. Problem:

A cup of water (approx. 250 ml) is heated from 25 to 100 C. Find the change in internal energy for the cup of water?


find:

dU = change in internal energy of the cup of water


given:

V = 250 mL ---> a cup of water

t1 = 25 C

t2 = 100 C ---> boiling point of water


Solution:

Cp of water = 4.2 J/g C

Density of water = 1 g/mL


m = D * V

m = 1 g/ml * 250 ml

m = 250 g


dU = m * Cp * dT

dU = 250 * 4.2 * (100 - 25)

dU = 250 * 4.2 * 75

dU = 78,750 J or 78.75 kJ


Thus, to boil a cup of water,

it requires approximately

80 kJ