latent heat of fusion of ice is 3.36exp5 j/kg and its specific heat is 1200j/mole.k.. 2kg of ice is at -10degC how much ice will be melt when a heat of 1.42exp5 joule is provided completely? a) 0.5kg b) 1.5kg c) 2kg d) 1kg
heat to warm ice=2*1200/mole*10= 2/18*1200*10= 1.3kJ
heat left over to
melt ice=142kJ-1.3 kJ=140kJ
melting ice:
140kJ=mass*336kJ
massmelted=140/336= about .4kg
closest answer is the lowest one.
To determine how much ice will melt when a heat of 1.42 x 10^5 joules is provided, we need to consider the heat required for both the change in temperature and the change in phase.
First, let's calculate the heat required to raise the temperature of the ice from -10°C to 0°C using its specific heat capacity. The formula for calculating heat is:
Q = m * c * ΔT
where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Given:
Mass of ice (m) = 2 kg
Specific heat capacity (c) = 1200 J/mole·K
Change in temperature (ΔT) = 0°C - (-10°C) = 10°C
Heat for temperature change (Q1) = m * c * ΔT
Next, we need to calculate the heat required to completely melt the ice. The formula for calculating the heat for the change in phase is:
Q = m * L
where Q is the heat energy, m is the mass, and L is the latent heat of fusion.
Given:
Mass of ice (m) = 2 kg
Latent heat of fusion (L) = 3.36 x 10^5 J/kg
Heat for phase change (Q2) = m * L
Finally, to find the total heat energy required, we can add the two heat values together:
Total heat energy required = Q1 + Q2
Substituting the values into the equations:
Q1 = 2 kg * 1200 J/mole·K * 10°C
Q2 = 2 kg * 3.36 x 10^5 J/kg
Total heat energy required = Q1 + Q2
Now let's calculate the values:
Q1 = 2 * 1200 * 10 = 24000 J
Q2 = 2 * 3.36 x 10^5 = 672000 J
Total heat energy required = 24000 + 672000 = 696000 J
Since we have 1.42 x 10^5 J of heat provided, we can divide the provided heat energy by the total heat energy required to find the fraction of ice that will melt:
Fraction of ice melted = Provided heat energy / Total heat energy required
Fraction of ice melted = 1.42 x 10^5 J / 696000 J
Fraction of ice melted ≈ 0.204
To find the mass of ice that will melt, we multiply the fraction of ice melted by the initial mass of ice:
Mass of ice melted = Fraction of ice melted * Initial mass of ice
Mass of ice melted = 0.204 * 2 kg
Mass of ice melted ≈ 0.408 kg
Rounding to the nearest tenth, the mass of ice that will melt when 1.42 x 10^5 J of heat is provided completely is approximately 0.4 kg.
So the correct answer is not provided in the options given.