Answer:
7.9060 m²
8.57 Volts
5.142×10⁻⁶ Joule
1.2×10⁻⁶ Coulomb
Explanation:
C = Capacitance between plates = 0.14 μF = 0.14×10⁻⁶ F
d = Distance between plates = 0.5 mm = 0.5×10⁻³ m
Q = Charge = 1.2 μC = 1.2×10⁻⁶ C
ε₀ = Permittivity = 8.854×10⁻¹² F/m
Capacitance
![C=\frac{\epsilon_{0}A}{d}\\\Rightarrow A=\frac{Cd}{\epsilon_{0}}\\\Rightarrow A=\frac{0.14\times 10^{-6}\times 0.5\times 10^{-3}}{8.854\times 10^{-12}}\\\Rightarrow A=7.9060\ m^2](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%5Cepsilon_%7B0%7DA%7D%7Bd%7D%5C%5C%5CRightarrow%20A%3D%5Cfrac%7BCd%7D%7B%5Cepsilon_%7B0%7D%7D%5C%5C%5CRightarrow%20A%3D%5Cfrac%7B0.14%5Ctimes%2010%5E%7B-6%7D%5Ctimes%200.5%5Ctimes%2010%5E%7B-3%7D%7D%7B8.854%5Ctimes%2010%5E%7B-12%7D%7D%5C%5C%5CRightarrow%20A%3D7.9060%5C%20m%5E2)
∴ Area of each plate is 7.9060 m²
Voltage
![V=\frac{Q}{C}\\\Rightarrow V=\frac{1.2\times 10^{-6}}{0.14\times 10^{-6}}\\\Rightarrow V=8.57\ Volts](https://tex.z-dn.net/?f=V%3D%5Cfrac%7BQ%7D%7BC%7D%5C%5C%5CRightarrow%20V%3D%5Cfrac%7B1.2%5Ctimes%2010%5E%7B-6%7D%7D%7B0.14%5Ctimes%2010%5E%7B-6%7D%7D%5C%5C%5CRightarrow%20V%3D8.57%5C%20Volts)
∴ Potential difference between the plates if the capacitor is charged to 1.2 μC is 8.57 Volts.
Energy stored
E=0.5CV²
⇒E = 0.5×0.14×10⁻⁶×8.57²
⇒E = 5.142×10⁻⁶ Joule
∴ Stored energy is 5.142×10⁻⁶ Joule
Charge
Q = CV
⇒Q = 0.14×10⁻⁶×8.57
⇒Q = 1.2×10⁻⁶ C
∴ Charge the capacitor carries before a spark occurs between the two plates is 1.2×10⁻⁶ Coulomb
<span>
<u><em>Answer:</em></u>498.82 cg is equivalent to 4988.2 mg
<u><em>Explanation:</em></u>cg stands form centigrams
mg stands for milligrams
From the standards of conversion, to convert from centi to milli, we multiply the amount ny 10
<u>This means that:</u>
1 centigram = 10 milligram
To convert 498.82 cg to mg, all we have to do is <u>cross multiplication</u> as follows:
1 cg ..................> 10 mg
498.82 cg .........> ?? mg
498.82 cg = </span>
![\frac{498.82*10}{1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B498.82%2A10%7D%7B1%7D%20)
<span> = 4988.2 mg
Hope this helps :)</span>
Answer:
712.5 J/g
5130000 J
618.421052632 cm³
Explanation:
= Specific heat = 0.46 J/g°C
= Change in temperature = (1300-25)°C
= Heat of fusion = 126 J/g
= Density = ![7.6\ g/cm^3](https://tex.z-dn.net/?f=7.6%5C%20g%2Fcm%5E3)
Unit energy for melting and pouring is given by
![Q=\Delta H_f+c_p\Delta T\\\Rightarrow Q=126+0.46(1300-25)\\\Rightarrow Q=712.5\ J/g](https://tex.z-dn.net/?f=Q%3D%5CDelta%20H_f%2Bc_p%5CDelta%20T%5C%5C%5CRightarrow%20Q%3D126%2B0.46%281300-25%29%5C%5C%5CRightarrow%20Q%3D712.5%5C%20J%2Fg)
The unit energy for melting and pouring is 712.5 J/g
Total energy is given by
![E=mc_p\Delta T+m\Delta H_f\\\Rightarrow E=7.2\times 10^3\times 0.46(1300-25)+7.2\times 10^3\times 126\\\Rightarrow E=5130000\ J](https://tex.z-dn.net/?f=E%3Dmc_p%5CDelta%20T%2Bm%5CDelta%20H_f%5C%5C%5CRightarrow%20E%3D7.2%5Ctimes%2010%5E3%5Ctimes%200.46%281300-25%29%2B7.2%5Ctimes%2010%5E3%5Ctimes%20126%5C%5C%5CRightarrow%20E%3D5130000%5C%20J)
The total energy of the process is 5130000 J
Volume is given by
![V=\dfrac{m}{\rho}\\\Rightarrow V=\dfrac{4700}{7.6}\\\Rightarrow V=618.421052632\ cm^3](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7Bm%7D%7B%5Crho%7D%5C%5C%5CRightarrow%20V%3D%5Cdfrac%7B4700%7D%7B7.6%7D%5C%5C%5CRightarrow%20V%3D618.421052632%5C%20cm%5E3)
The volume of the casting is 618.421052632 cm³