Heat Capacity and Temperature Change Calculations

This page delves into the practical application of the Q = mCpΔT formula for temperature changes within a single phase.

Example: Heating water from 3°C to 89°C requires using the liquid phase specific heat since the entire temperature range falls between water's freezing point (0°C) and boiling point (100°C).

Definition: Q (heat/enthalpy) represents energy transfer in a system, measured in Joules.

Key variables explained:

• m = mass (in grams)
• Cp = specific heat (phase-dependent)
• ΔT = temperature change (in °C)

Practical Heat Calculations

This page demonstrates practical applications through worked examples.

Example: Calculating energy needed to raise 50g of water from 3°C to 89°C: Q = (50g)(4.184 J/g°C)(86°C) = +17,991.25J

Example: Energy needed to cool 150g of water from 57°C to 1°C: Q = (150)(4.184)(-56) = -35,145.65J

The negative value indicates energy removal for cooling.

Phase Change Energy Calculations

This page introduces phase change energy calculations using Q = mΔHv or Q = mΔHf.

Definition: ΔHf represents energy needed for solid-liquid phase changes at melting point Definition: ΔHv represents energy needed for liquid-gas phase changes at boiling point

Highlight: Phase changes occur at constant temperature, requiring energy input/removal for the entire mass.

Complex Temperature and Phase Change Problems

This final section demonstrates how to solve problems involving both temperature changes and phase transitions.

Example: For changing 50g of water from -2°C to 89°C, the solution requires three steps:

1. Heating solid (-2°C to 0°C)
2. Phase change at 0°C
3. Heating liquid (0°C to 89°C)

Highlight: All values should be positive when increasing temperature and moving up the heating curve.