How much heat is required to raise 75 grams of 0 degree Celsius ice to 135 degree Celsius steam?
to get the heat released or absorbed,
Q = mc(T2-T1)
where
m = mass of substance (units in g)
c = specific heat capacity (units in J/g-K)
T2 = final temperature
T1 = initial temperature
**note: if Q is (-), heat is released and if (+), heat is absorbed
now we can only apply this to substances that did not change its phase, but in the problem, we see that phase change occurs. from ice->water->steam
thus we need another data called it Latent Heat of Fusion and Latent Heat of Vaporization to calculate for the heat required to change its phase:
H1 = m(Lf)
H2 = m(Lv)
where
m = mass
Lf = Latent Heat of Fusion (fusion means melting)
Lv = Latent Heat of Vaporization (vaporization means from liquid, it becomes vapor)
the heat required to raise the LIQUID's temp (from 0 C to 100 C) is
Q1 = mc(100 - 0) = 100*75*c = 7500*c
the heat required to raise the STEAM's temp (from 100 to 135) is
Q2 = mc(135 - 100) = 35*75*c
thus the total heat needed is:
Q,total = H1 + Q1 + H2 + Q2
note that can find c, Lf and Lv of water in books or you can just google it. remember and be careful of the units.
hope this helps~ :)
To calculate the amount of heat required to raise the temperature of a substance, you need to consider two separate processes: heating the substance from its initial temperature to its melting point, and then converting it from a solid to a liquid, and then from a liquid to a gas.
Let's break down the calculation step by step:
1. Heating the ice from 0°C to its melting point:
The specific heat capacity of ice is 2.09 J/g°C. This means that it takes 2.09 Joules of energy to raise the temperature of 1 gram of ice by 1 degree Celsius.
The temperature change required is: 0°C → melting point of ice (0°C)
So the heat required to raise the temperature of the ice can be calculated using the formula:
Q1 = mass × specific heat capacity × temperature change
Q1 = 75 g × 2.09 J/g°C × (melting point of ice - 0°C)
2. Melting the ice to liquid water:
For this process, we need to consider the heat of fusion, which is the amount of energy required to convert a substance from a solid to a liquid at its melting point. For water, the heat of fusion is 334 J/g.
The heat required to melt the ice can be calculated using the formula:
Q2 = mass × heat of fusion
Q2 = 75 g × 334 J/g
3. Heating the liquid water from its melting point to 100°C:
The specific heat capacity of water is 4.18 J/g°C.
The temperature change required is: melting point of ice (0°C) → 100°C
So the heat required to raise the temperature of liquid water can be calculated using the formula:
Q3 = mass × specific heat capacity × temperature change
Q3 = 75 g × 4.18 J/g°C × (100°C - melting point of ice)
4. Vaporizing the water to steam at 100°C:
For this process, we need to consider the heat of vaporization, which is the amount of energy required to convert a substance from a liquid to a gas at its boiling point. For water, the heat of vaporization is 2260 J/g.
The heat required to convert liquid water to steam can be calculated using the formula:
Q4 = mass × heat of vaporization
Q4 = 75 g × 2260 J/g
To find the total heat required, we add up the individual amounts of heat:
Total heat required = Q1 + Q2 + Q3 + Q4
Now you can calculate the answer by plugging in the numbers for the respective variables and performing the calculations. This will give you the total amount of heat required to raise 75 grams of ice from 0°C to steam at 100°C.