the amount of heat energy required to convert 5g of ice at 0 degree centigrade into water at 40 degree centigrade is
Q= L m+ cm•Δt = m(L+c•Δt)=
=0.005(334000+4184•40)=1678.2 J
To calculate the amount of heat energy required to convert 5g of ice at 0 degrees Celsius into water at 40 degrees Celsius, we need to consider the two phases involved: the phase change from ice to water and the subsequent heating of the water.
1. Phase change from ice to water:
The heat energy required for this phase change is given by the equation:
Q1 = mass × specific heat capacity × latent heat of fusion
where Q1 is the heat energy required, mass is the mass of the substance, specific heat capacity is the specific heat capacity of the substance, and latent heat of fusion is the latent heat of fusion of the substance.
For ice at 0 degrees Celsius, the specific heat capacity is 2.09 J/(g°C) and the latent heat of fusion is 334 J/g.
Q1 = 5g × 2.09 J/(g°C) × 334 J/g
Q1 = 3,505 J
So, the heat energy required for the phase change from ice to water is 3,505 J.
2. Heating the water from 0 degrees Celsius to 40 degrees Celsius:
The heat energy required to heat a substance can be calculated using the equation:
Q2 = mass × specific heat capacity × temperature change
where Q2 is the heat energy required, mass is the mass of the substance, specific heat capacity is the specific heat capacity of the substance, and temperature change is the change in temperature.
For water, the specific heat capacity is 4.18 J/(g°C).
Q2 = 5g × 4.18 J/(g°C) × (40 - 0)°C
Q2 = 836 J
So, the heat energy required to heat the water from 0 degrees Celsius to 40 degrees Celsius is 836 J.
Adding the energies from both processes together:
Total heat energy = Q1 + Q2
Total heat energy = 3,505 J + 836 J
Total heat energy = 4,341 J
Therefore, the amount of heat energy required is 4,341 J.
To calculate the amount of heat energy required to convert 5g of ice at 0 degrees Celsius into water at 40 degrees Celsius, you need to follow these steps:
1. Calculate the heat energy required to melt the ice: This can be done using the formula Q = m * Lf, where Q is the heat energy, m is the mass of the substance, and Lf is the latent heat of fusion. For ice, the latent heat of fusion is 334 J/g. Therefore, Q1 = 5g * 334 J/g.
2. Calculate the heat energy required to raise the temperature of the melted ice to 40 degrees Celsius: This can be done using the formula Q = m * c * ΔT, where Q is the heat energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature. For water, the specific heat capacity is 4.18 J/g°C. Therefore, Q2 = 5g * 4.18 J/g°C * (40°C - 0°C).
3. Add the two results together to get the total heat energy required: Q_total = Q1 + Q2.
Let's calculate the answer:
Q1 = 5g * 334 J/g = 1670 J
Q2 = 5g * 4.18 J/g°C * 40°C = 836 J
Q_total = 1670 J + 836 J = 2506 J
Therefore, the amount of heat energy required to convert 5g of ice at 0 degrees Celsius into water at 40 degrees Celsius is 2506 Joules.