Where did i go wrong in fudingin the temperature of the gold cube?

[yjk91]

Homework Statement

A cube of gold (resistivity ?R = 2.44 10-8 O m, density ?D = 1.93 104 kg / m3, and specific heat c = 129 J / kg °C) that is 3.5 mm on a side is connected across the terminals of a 40-µF capacitor that initially has a potential difference of 340.0 V between its plates.

http://www.webassign.net/bauerphys1/26-p-052.gif

(b) When the capacitor is fully discharged, what is the temperature of the gold cube? (Use 20°C for room temperature.

The Attempt at a Solution

i found R = p L /A

and got 0.69714 * 10^-5 ohm

Q = C *V = 40 *10^-6 * 340 V = 136 * 10^-4 C

I = V/R = 340 / (0.69714 * 10^-5) = 487.7066 * 10^5 A

time t = Q/I = 136*10^-4 / (487.706*10^5) = 0.27885 * 10^-9s

E = V^2t/R = 340^2(0.27885*10e-9) / 0.69714e-5
= 4.6239 J

m = density * volume = 1.93 * 10e4 * 3.5*e-3^3 =82.74875e-5 kg

E = mc delta T

T = E/(mc) = 4.6239 / (82.74875e-5*129) = 43

Tf = 43+20= 63mm where did i go wrong?

 

[gneill]

You're taking the long way around to calculate the energy deposited in the gold, and there are some assumptions being made that look somewhat dubious.

Why don't you assume that all the energy initially stored in the capacitor will be dumped into the gold (the capacitor will have zero charge, thus zero energy when its fully discharged, so that energy must have gone into heating the gold).

Given the capacitance and voltage, what's the energy stored in the capacitor?

 

[yjk91]

sweet i got it thx

 

[yjk91]

You're taking the long way around to calculate the energy deposited in the gold, and there are some assumptions being made that look somewhat dubious.

Why don't you assume that all the energy initially stored in the capacitor will be dumped into the gold (the capacitor will have zero charge, thus zero energy when its fully discharged, so that energy must have gone into heating the gold).

Given the capacitance and voltage, what's the energy stored in the capacitor?

hey Gneli
could you help me with this problem? i just need a place to start and some guidance

thank you
https://www.physicsforums.com/showthread.php?p=3419623#post3419623

 

[rwisz]

There are a few potential errors in your calculation. First, when calculating the resistance (R), you used the wrong units for length (L). The correct units should be meters (m), not millimeters (mm). This would change your value for R to 0.69714 x 10^-8 ohm, which would then affect all subsequent calculations.

Additionally, the value for current (I) that you calculated is incorrect. The correct value should be 340 / (0.69714 x 10^-8) = 487.7066 x 10^-5 A. This would then change the value for time (t) to 0.27885 x 10^-6 s and the value for energy (E) to 4.6239 x 10^-6 J.

Another potential error is in your calculation of mass (m). The correct units for volume should be cubic meters (m^3), not cubic millimeters (mm^3). This would change your value for mass to 82.74875 x 10^-9 kg.

Finally, when calculating the final temperature (Tf), you used the incorrect value for specific heat (c). The correct value should be 129 J / kg K, not 129 J / kg °C. This would change your final value for temperature to 53 K.

In summary, to correct your calculation, you would need to use the correct units for length, volume, and specific heat, and make sure to use the correct value for current.