Respuesta :
Answer:
Explanation:
specific heat of granite s = .79 J / g / k
let the mass of granite = m
heat lost by granite = heat gained by water
heat lost = mass x specific heat x drop in temperature
= m x .79 x (80 - 20.45)
heat gained by water
= 3000 x 4.186 x (20.45- 20)
heat lost by granite = heat gained by water
m x .79 x 59.55 = 3000 x 4.186 x .45
m = 120.12 g .
The mass of granite is approximately equal to 120 g.
The specific heat capacity refers to the amount of energy required or needed to raise the temperature of 1 gram of a material or substance by 1° C.
Let assume that:
- the mass of the water is 1000 g at 2.93 °C
The heat energy gained by water can be calculated using the formula:
Q = mcΔT
where;
m = mass = 1000 g
c = specific heat = 4.183 J/g° C
ΔT = change in temperature
Q = 1000 g × 4.183 J/g° C × (2.93 - 0)° C
Q = 1000 g × 4.183 J/g° C × (2.93) ° C
Q = 12256.19 J
Q = 12.256 kJ
The next step is to determine the specific heat of granite.
Since;
The heat gained by water = Heat lost by granite.
The heat lost by granite = 12.256 kJ
Using the relation;
Q = mcΔT
Making (c) the subject of the formula:
[tex]\mathbf{c = \dfrac{Q}{m \Delta T}}[/tex]
[tex]\mathbf{c = \dfrac{12.256 \ kJ}{200 \times (100 - 22.93)^0 \ C}}[/tex]
[tex]\mathbf{c = \dfrac{12.256 \times 10^3 \ J}{200 \ g \times (77.07)^0 \ C}}[/tex]
[tex]\mathbf{c = 0.795 \ J/g^0 \ C }[/tex]
The specific heat of granite = 0.795 J/g° C
Recall from the given parameters;
- initial temperature of granite = 80°C
- initial temperature of water = 20°C
∴
Again, heat gained by water = heat lost by granite
[tex]\mathbf{m_{water} \times c_{water} \times \Delta T= m_{granite} \times c_{granite} \times \Delta T}[/tex]
To determine the mass of granite, make [tex]\mathbf{m_{granite} }[/tex] the subject of the formula;
i.e.
[tex]\mathbf{ m_{granite}= \dfrac{m_{water} \times c_{water} \times \Delta T}{c_{granite} \times \Delta T} }[/tex]
[tex]\mathbf{ m_{granite}= \dfrac{3000 g \times 4.184 \ J/g^0 \ C \times (20.45 - 20)^0 \ C}{0.795 J/g^0 \ C \times(80-20.45)^0 \ C} }[/tex]
[tex]\mathbf{ m_{granite}= \dfrac{5648.4 g}{47.34225} }[/tex]
[tex]\mathbf{ m_{granite}=119.31 \ g }[/tex]
Therefore, we can conclude that the mass of granite is approximately equal to 120 g.
Learn more about specific heat capacity here:
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