joules needed to melt a 525 g ice cube at 0 degree C and to warm the liquid to 15 degrees C (two steps please show work)
To calculate the total energy required to melt the ice cube and then warm the resulting liquid, we need to consider the energy required for each step separately. We can use the specific heat capacity and the heat of fusion of water for these calculations. Here's how you can calculate it step by step:
Step 1: Melting the ice cube
To melt the ice cube, we need to calculate the energy required for the phase change from solid to liquid. The formula is:
Q = m * ΔHf
where:
Q = energy required (in joules)
m = mass of the ice cube (in grams)
ΔHf = heat of fusion of water (in J/g)
The heat of fusion of water is typically 334 J/g.
Let's calculate:
m = 525 g
ΔHf = 334 J/g
Q = 525 g * 334 J/g
Q = 174,150 J (or 174.15 kJ)
So, to melt the ice cube, we need approximately 174,150 joules (or 174.15 kJ) of energy.
Step 2: Warming the liquid
To warm the liquid to a specific temperature, we need to calculate the energy required using the formula:
Q = m * c * ΔT
where:
Q = energy required (in joules)
m = mass of the liquid (in grams)
c = specific heat capacity of water (in J/g°C)
ΔT = change in temperature (in °C)
The specific heat capacity of water is about 4.18 J/g°C.
Let's calculate:
m = 525 g (assuming no evaporation during melting)
c = 4.18 J/g°C
ΔT = 15°C - 0°C = 15°C
Q = 525 g * 4.18 J/g°C * 15°C
Q = 32,967.5 J (or 32.97 kJ)
So, to warm the liquid from 0°C to 15°C, we need approximately 32,967.5 joules (or 32.97 kJ) of energy.
Therefore, the total energy required to melt the ice cube and warm the liquid is the sum of the energy required for each step:
Total energy = Energy to melt the ice cube + Energy to warm the liquid
Total energy = 174,150 J + 32,967.5 J
Total energy = 207,117.5 J (or 207.12 kJ)
Hence, the total energy required is approximately 207,117.5 joules (or 207.12 kJ).
q1 = heat to melt ice
q1 = mass ice x heat fusion
q2 = heat to raise T from zero C to 15 C.
q2 = mass melted ice x specific heat H2O x (Tfinal-Tinitial)
Total = q1 + q2.