Gold has a very low specific heat capacity, just 0.13 J/goC. If a gold class ring has a mass of 4 grams and is heated from 0oC to 100oC, what is the amount of energy the gold class ring has absorbed? a 52 Joules b 0.325 Joules c 400 Joules d 3076.92 Joules

a 52 Joules

Explanation:

Specific heat capacity of Au = 0.13 J/g° C

mass = 4 gram

initial temperature = 0° C

final temperature = 100° C

We are to determine the amount of energy absorbed

Using the formula:

Q = mcΔθ

Q = 4 × (0.13) J/g° C ×(100-0)

Q = 52 Joules

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

8 m/s because for him to get the same amount of energy as ray is putting out, bobby, who weighs half as much as ray, needs to run twice as fast.