#"2659 J"# of heat energy are required to heat a substance with a mass of #"24.25 g"# from #"23.7"^@"C"# to #"163.5"^@"C"#. What is its specific heat capacity?
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So, the equation we are using is #Q = mcDeltaT#.
=> Where #Q# is the amount of thermal energy in joules, #J#.
=> Where #m# is the mass in kilograms, #kg#.
=> Where #c# is the specific heat capacity.
=> Where #DeltaT# is the change in temperature in degrees Celsius.
#24.25 g = 0.02425 kg#
#Q = mcDeltaT#
#Q = mc (T_2-T_1)#
#"2659 J" = "0.02425 kg"xxcxx"(163.5 - 23.7) °C"#
#"2659 J" = "0.02425 kg"xxcxx"139.8 °C"#
#"19.02 J/°C"= "0.02425 kg"xxc#
#c = "784.3 J/(°C·kg)"#
The specific heat capacity is #784.3 J/(°C·kg)#.
Hope this helps :)
Apply the equation #Q=mcDeltaT#, where #Q# is the energy in Joules, #m# is the mass in grams, #c# is the specific heat, and #DeltaT# is change in temperature. #DeltaT=T_"final"-T_"initial"#
Known
#Q="2659 J"#
#m="24.25 g"#
#T_"initial"="23.7"^@"C"#
#T_"final"="163.5"^@"C"#
#DeltaT="163.5"^@"C"-"23.7"^@"C"="139.8"^@"C"#
Unknown
#c#
Solution
Rearrange the equation #Q=mcDeltaT# to isolate #c#. Substitute the known values into the equation and solve.
#c=(Q)/(m*DeltaT)#
#c=(2659"J")/(24.25"g"*139.8^@"C")#
#c=0.7843"J"/("g"*^@"C")#
