Part A

Find the energy U0 stored in the capacitor. Express your answer in terms of A, d, V, and ϵ0. Remember to enter ϵ0 as epsilon0.

Part B

The capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches 3d. Find the new energy U1 of the capacitor after this process.

Express your answer in terms of A, d, V, and ϵ0.

Part C

The capacitor is now reconnected to the battery, and the plate separation is restored to d. A dielectric plate is slowly moved into the capacitor until the entire space between the plates is filled. Find the energy U2 of the dielectric-filled capacitor. The capacitor remains connected to the battery. The dielectric constant is K.

Express your answer in terms of A, d, V, K, and ϵ0.

A 580-mm long tungsten wire, with a 0.046-mm-diameter circular cross section, is wrapped around in the shape of a coil and used as a filament in an incandescent light bulb. When the light bulb is connected to a battery, a current of 0.526 A is measured through the filament. (Note: tungsten has a resistivity of 4.9 × 10-8 ? • m.) How many electrons pass through this filament in 5 seconds?

How many electrons pass through this filament in 5 seconds? 4.22 × 10-19 2.63 3.29 × 1018 1.64 × 1019

What is the resistance of this filament? What is the resistance of this filament? 4.28 ? 58.5 m? 17.1 ? 9.0 ?

What is the voltage of the battery that would produce this current in the filament? 31 mV 9.0 V 2.6 × 10-8 V 32 V

This is an astronomy question:

Two stars, both with surface temperatures of 9700 K, deposit 1000 photons/second and 3200 photons/second on our detector (of unit size), respectively, when observed with a V filter (visual).

(a) How do their V-band magnitudes compare (i.e. what is V1 - V2)?

(b) How do their B magnitudes compare?

Student's note: I'm deeply confused on how to even begin this. Please show work so I can understand this. It's not clear to me whether I'm supposed to do a calculation to determine V magnitudes and B magnitudes knowing only temp and flux or whether I'm supposed to be looking something up on a table somewhere. I just don't know where to start. Thank you

A phase transition from solid to liquid takes place at constant pressure and temperature. This is a closed PVT system. (a) Show that the Gibbs free energy G = U - TS + PV is a constant. (b) The solid and liquid phases are in equilibrium at a temperature T and pressure P, where G(solid) = G(solid)(T,P) and G(liquid) = G(liquid)(T,P). The phases are also in equilibrium at the neighboring temperature T +dT and pressure P + dP, where G(solid) = G(solid)(T+dT, P+dP) and G(liquid) = G(liquid)(T+dT, P+dP). Show that at temperature T, (dP/dT) = (S(liquid) - S(solid)) / (V(liquid) - V(solid)) where S and V denote entropy and volume respectively.

(b) You will titrate 25.00mL of Histidine dihydrochloride solution of unknown concentration with the secondary standard NaOH. Use a value of 0.025M Histidine dihydrochloride to estimate the volume of NaOH required to completely deprotonate the histidine dihydrochloride. The concentration of NaOH is .1254 M. This calculated volume is an estimate of the third equivalence point. Use this value to estimate the first and second equivalence point volumes.

(c) Calculate the volumes at ~75% and ~90% of the three approximated equivalence points and record these values in the copied Data Table F from your manual pages.

Data Table F: Calc approximate volumes to reach endpoint

At time t’=0.4 ms, as measured by Alice, in the coordinate system K’, a particle is at the point x’=10 m, y’= 4m, z’=6m. (Note that this constitutes an event). Compute the corresponding values of x,y,z,t, as measured by Bob in coordinate system K, for

(a) the velocity of K’ relative to K along the common xx’ axis is v= +500 m/s

(b) the velocity of K’ relative to K along the common xx’ axis is v= −500 m/s and

(c) the velocity of K’ relative to K along the common xx’ axis is v= 2×108 m/s

(d) when you compare the answers of the different cases what do you notice about the role of the magnitude of the relative velocity (especially when comparing the results of a and b with the result of c)?

In the following spontaneous reaction, the mercuric ion is:

Hg²⁺ + Cu → Hg + Cu²⁺

Question options:

Based on the following reduction potential data, which is the strongest oxidizing agent?
E°_red = +1.78 V for H₂O₂(aq) + 2H⁺(aq) + 2e^- → 2H₂O(l)

E°_red = +0.800 V for Ag⁺(aq) + e^- → Ag(s)
E°_red = -0.130 V for Pb²⁺(aq) + 2e^- → Pb(s)

Question options:

hich of the following statements are FALSE?

Which of the following statements are FALSE?

An outbreak of Vibrio vulnificus occurred in people that ate oysters from a local restaurant. The oysters were traced backed to a farm that grows oysters in four separate salt-water ponds. You want to use PCR to determine which ponds are contaminated with V. vulnificus so you can decontaminate them. After collecting water samples from each pond and isolating the DNA from each sample, you perform PCR using V. vulnificus specific primers and obtain the results shown below.

A. What do you need in order to run the PCR besides your primers (things that go in the PCR and the thing that the PCR goes in)?

B. What makes your primers specific to V. vulnificus?

C. Based on the PCR results above, which pond (if any) should be decontaminated?