Answer :
Answer:
The mass of silver block = 73.95 g
Explanation:
Given,
For water:
Mass = 100.0 g
Initial temperature = 24.8 °C
Final temperature = 26.2 °C
Specific heat of water = 4.184 J/g°C
For silver:
Mass = x g
Initial temperature = 59.4 °C
Final temperature = 26.2 °C
Specific heat of water = 0.2386 J/g°C
Heat gain by water = Heat lost by silver
Thus,
[tex]m_{water}\times C_{water}\times (T_f-T_i)=-m_{silver}\times C_{silver}\times (T_f-T_i)[/tex]
Where, negative sign signifies heat loss
Or,
[tex]m_{water}\times C_{water}\times (T_f-T_i)=m_{silver}\times C_{silver}\times (T_i-T_f)[/tex]
So, [tex]100.0\times 4.184\times (26.2-24.8)=x\times 0.2386\times (59.4-26.2)[/tex]
[tex]x\times \:0.2386\left(59.4-26.2\right)=100\times \:4.184\left(26.2-24.8\right)[/tex]
[tex]x\times \:0.2386\left(59.4-26.2\right)=585.76[/tex]
[tex]x=\frac{585.76}{7.92152}[/tex]
[tex]x=73.95[/tex]
Hence, the mass of silver block = 73.95 g
The mass of the silver block is equal to 73.95 grams.
Given the following data:
- Initial temperature of silver = 59.4°C
- Mass of water = 100.0 g
- Initial temperature of water = 24.8°C
- Final temperature of water = 26.2°C
- Final temperature of silver = 26.2°C
Specific heat of silver = 0.2386 J/g°C
Specific heat of water = 4.184 J/g°C
To find the mass of the silver block:
Mathematically, quantity of heat is given by the formula;
[tex]Q = mc\theta[/tex]
Where:
- Q represents the quantity of heat.
- m represents the mass of an object.
- c represents the specific heat capacity.
- ∅ represents the change in temperature.
The quantity of heat lost by the silver block = The quantity of heat gained by the water.
[tex]Q_{lost} = Q_{gained}\\\\mc\theta = mc\theta\\\\m(0.2386)(59.4 - 26.2) = 100(4.184)(26.2 -24.8)\\\\m(0.2386)(33.2) = 418.4(1.4)\\\\7.9215m = 585.76\\\\m = \frac{585.76}{7.9215}[/tex]
Mass, m = 73.95 grams
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