The temperature of 50.0 g of water was raised to 50.0°C by the addition of 1.0 kJ of heat energy. What was the initial temperature of the water?

Question

Owen Ambrose · Accepted Answer

#45.2^@"C"#

The idea here is that in order to determine the resulting change in temperature, you need to know the mass of water, the amount of heat added to the sample, and the specific heat of water.

This is the equation that shows the connection between heat absorbed and temperature change.

#color(blue)(q = m * c * DeltaT)" "#, where

#q# - heat absorbed #m# - the mass of the sample #c# - the specific heat of water, equal to #4.18"J"/("g" ""^@"C")# #DeltaT# - the change in temperature, defined as final temperature minus initial temperature

Plug in your values and solve for #DeltaT# - do not forget to convert the added heat from kilojoules to Joules

#q = m * c * DeltaT implies DeltaT = q/(m * c)#

#DeltaT = (1.0 * 10^(3)color(red)(cancel(color(black)("J"))))/(50.0color(red)(cancel(color(black)("g"))) * 4.18color(red)(cancel(color(black)("J")))/(color(red)(cancel(color(black)("g"))) ""^@"C")) = 4.785^@"C"#

So, if the temperature of the water changed by #4.785^@"C"#, and its final temperature is now #50.0^@"C"#, it follows that its initial temperature was

#DeltaT = T_"f" - T_"i" implies T_"i" = T_"f" - DeltaT#

#T_"i" = 50.0^@"C" - 4.785^@"C" = color(green)(45.2^@"C")#

Cameron Andrews · Answer

undefined To find the initial temperature of the water, you can use the formula:

q = mcΔT

where:
q = heat energy (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (final temperature - initial temperature)

Given:
q = 1.0 kJ = 1000 J
m = 50.0 g
c = specific heat capacity of water = 4.18 J/g°C
ΔT = 50.0°C - initial temperature

Rearranging the formula to solve for initial temperature:

Initial temperature = final temperature - (q / (m * c))

Plugging in the values:

Initial temperature = 50.0°C - (1000 J / (50.0 g * 4.18 J/g°C)) = 50.0°C - 4.78°C = 45.22°C

Therefore, the initial temperature of the water was approximately 45.22°C.