A sample of mercury absorbed 257 J of heat and its mass was .45 kg. If it's temperature increased by 4.09 K, what is its specific heat in J° / kg K?

2 Answers
Jan 18, 2017

The specific heat formula is:

#c = Q/(m × ΔT)#

Where:

#c#: specific heat, in J/(kg.K)

#Q#: heat required for the temperature change, in J

#ΔT#: temperature change, in K

#m#: mass of the object, in kg

For our equation, we are given everything in the right units, so all we need is to plug in the numbers.

#c = Q/(m × ΔT)#

#c = (257)/(.45 xx 4.09)#

#c = 139.64 (J)/(kgxxK)#

Jan 18, 2017

Answer:

The specific heat of mercury to two significant figures is #"140 J"/("kg"*"K")#.

Explanation:

Use the equation #color(red)(Q=mcDeltat)#, where #Q# is energy gained or lost in Joules; #m# is mass, in this case kg; #c# is specific heat, in this case in #"J"/("kg"*"K")"#; and #Deltat# is change in temperature, in this case Kelvins.
Determine what variables are known, and unknown. Then solve the equation for the unknown variable.

Known
#Q="257 K"#
#m="0.45 kg"#
#Deltat="4.09 K"#

Unknown
#c_"Hg"#

Solution
Rearrange the equation to isolate #c_"Hg"#. Substitute the known values into the equation and solve.

#c_"Hg"=(Q)/(m*Deltat)=(257"J")/((0.45"kg")xx(4.09"K"))="140 J"/("kg"*"K")# rounded to two signficant figures