If 42.0 kJ of heat is added to a 32.0-g sample of liquid meth-ane under 1 atm of pressure at a temperature of -170°C, what are the final state and temperature of the methane once the system equilibrates? Assume no heat is lost to the surroundings. The normal boiling point of methane is -161.5 °C. The specific heats of liquid and gaseous methane are 3.48 and 2.22 J/g-K, respectively. [Section 11.3]

Key Concepts

Heat Transfer and Temperature Change

Heat transfer refers to the movement of thermal energy from one object to another, which can result in a change in temperature. In this scenario, adding 42.0 kJ of heat to the methane will increase its temperature until it reaches its boiling point or undergoes a phase change. The specific heat capacities of the liquid and gaseous states of methane are crucial for calculating the temperature change during heating.

Phase Changes and Boiling Point

Phase changes occur when a substance transitions between solid, liquid, and gas states, often involving energy changes. The boiling point of a substance is the temperature at which it transitions from liquid to gas at a given pressure. For methane, the normal boiling point is -161.5 °C, and understanding this is essential to determine whether the added heat will cause the methane to boil or remain in the liquid state.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). For methane, the specific heat capacities for liquid and gas are 3.48 J/g-K and 2.22 J/g-K, respectively. This property is vital for calculating how much the temperature of the methane will increase with the added heat and whether it will reach the boiling point before transitioning to gas.