The specific heat capacity of solid zinc is 0.388 J g
°
C (a) Determine the amount of heat energy that is a5sociated with heating a 11.0-g sample of solid zinc from 23.5
°
C to 36.5
°
C. (b) Caleulate the final temperature teached when 284 J of heat is added to a 20.8 g sample of solid zinc initially at 23.5%C
The Correct Answer and Explanation is :
(a) Determining the Heat Energy for Heating Zinc
To calculate the heat energy required to heat a 11.0-g sample of solid zinc from 23.5°C to 36.5°C, we use the formula:
[ Q = m \times c \times \Delta T ]
Where:
- ( Q ) is the heat energy (in joules)
- ( m ) is the mass of the zinc sample (in grams)
- ( c ) is the specific heat capacity of zinc (in J/g°C)
- ( \Delta T ) is the change in temperature (in °C)
Given:
- ( m = 11.0 \, \text{g} )
- ( c = 0.388 \, \text{J/g°C} )
- ( \Delta T = 36.5°C – 23.5°C = 13.0°C )
Substituting these values into the formula:
[ Q = 11.0 \, \text{g} \times 0.388 \, \text{J/g°C} \times 13.0°C ]
Calculating:
Therefore, the heat energy required is approximately 55.48 joules.
(b) Calculating the Final Temperature After Adding Heat
To find the final temperature when 284 J of heat is added to a 20.8-g sample of solid zinc initially at 23.5°C, we rearrange the heat energy formula to solve for the final temperature (( T_f )):
[ Q = m \times c \times (T_f – T_i) ]
Rearranging to solve for ( T_f ):
[ T_f = \frac{Q}{m \times c} + T_i ]
Given:
- ( Q = 284 \, \text{J} )
- ( m = 20.8 \, \text{g} )
- ( c = 0.388 \, \text{J/g°C} )
- ( T_i = 23.5°C )
Substituting these values into the equation:
[ T_f = \frac{284 \, \text{J}}{20.8 \, \text{g} \times 0.388 \, \text{J/g°C}} + 23.5°C ]
Calculating:
Therefore, the final temperature reached is approximately 58.69°C.
Explanation
The specific heat capacity (( c )) of a substance indicates how much heat energy is required to raise the temperature of a unit mass of the substance by one degree Celsius. For zinc, this value is 0.388 J/g°C.
In part (a), we calculated the heat energy required to heat a 11.0-g sample of zinc from 23.5°C to 36.5°C. By applying the formula ( Q = m \times c \times \Delta T ), we determined that 55.48 joules of heat energy are needed.
In part (b), we calculated the final temperature after adding 284 J of heat to a 20.8-g sample of zinc initially at 23.5°C. By rearranging the heat energy formula to solve for the final temperature, we found that the final temperature reached is approximately 58.69°C.
These calculations demonstrate how the specific heat capacity of a material influences the amount of heat energy required to change its temperature.