How Do You Calculate the Capacitance of a Capacitor?

[RedBarchetta]

Homework Statement

A capacitor is charged until it holds 5.0 J of energy. It is then connected across a 10-k$$\Omega$$ resistor. In 8.6 ms, the resistor dissipates 2.0 J. What is the capacitance?

Homework Equations

Q=CV
U=(1/2)CV$$^{2}$$

The Attempt at a Solution

I'm not quite sure what do with this one. I have resistance, and a time period but can't figure out how to get charge or voltage from the energy values provided to then find the capacitance. If someone could guide me in the right direction I would greatly appreciate it.

Thank you!

 

[Gear300]

U = (1/2)CV² = q²/(2C).
Assuming the system consists only of a capacitor and resistor, in which the capacitor is discharging, then q(t) = Qe^-t/(RC), in which q(t) is the charge in the capacitor at time t and Q is the initial charge (when the capacitor was at 5J). Since capacitance is constant, the energy in the capacitor may be written as U(t) = (q(t))²/(2C) = Q²/(2C) * e^-2t/(RC). The Q²/(2C) in the expression for U(t) is apparently the expression for the initial energy, which was 5J. You know that the change in the energy was 2J, which means U(t) is 3J at the moment, and you also know the value of R and t. Thus, you could solve for C.