If the specific heat of water is 4.180 J/(g/°C), what mass of water can be heated from 5.0 °C to 80°C by 27.0 kJ of heat?
q = 27,000 = mass H2O x specific heat H2O x (Tfinal-Tintial)
To find the mass of water that can be heated, we can use the equation:
q = m * c * ΔT
where:
q = heat energy (in J)
m = mass of water (in g)
c = specific heat of water (in J/(g/°C))
ΔT = change in temperature (in °C)
Given:
q = 27.0 kJ = 27.0 * 1000 J
c = 4.180 J/(g/°C)
ΔT = (80 - 5) = 75 °C
Substituting the values into the equation, we get:
27.0 * 1000 J = m * 4.180 J/(g/°C) * 75 °C
Simplifying the equation:
27.0 * 1000 J = m * 313.5 J/g
Dividing both sides of the equation by 313.5 J/g:
m = (27.0 * 1000 J) / (313.5 J/g)
m = 86.238 g
Therefore, the mass of water that can be heated from 5.0 °C to 80 °C by 27.0 kJ of heat is approximately 86.2 g.
To find the mass of water that can be heated, we can use the equation Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. In order to find the mass, we can rearrange the equation:
m = Q / (cΔT)
Given that Q = 27.0 kJ = 27,000 J, c = 4.180 J/(g/°C), ΔT = 80°C - 5.0°C = 75°C, we can substitute these values into the equation:
m = 27,000 J / (4.180 J/(g/°C) * 75°C)
Calculating this expression will give us the mass of water that can be heated.