Question

A wedding ring has a mass of 7.804 grams and is made of gold and silver. When the ring has been heated to 96.53

Answer 1

let Mass of Ring be M

mass of gold in the ring me m

so

mass of silver in the ring = M-m

we know that

heat lost by hot body = heat gained by body

in this case

heat lost by ring = heat gained by water

we also know that

heat = mass x specific heat x temp change

so

heat lost by ring = heat gained by water

(ms x Ss x dTs )+ (mg x Sg x dTg) = mw x sw x dTw

temp change is same for both gold and ring

so

dTs = dTg

dTs ( Ms x Ss + mg x sg ) = mw x sw x dTw

[ (M-m) x 0.234 + m x 0.129 ) ] (96.53 -23.75 ) = 13.5 x 4.184 x ( 23.75 -21.73 )

solving we get

0.234M - 0.105m   = 1.5677

given

mass of ring M = 7.804 g

so

0.234 x 7.804 - 0.105m = 1.5667

m = 2.47

so the

mass of gold in the ring = 2.47 g

mass of silver in the ring = 7.804 - 2.47 = 5.334

we know that

mass% = ( mass of component / total mass ) x 100

mass% of gold = ( 2.47 / 7.804 ) x 100

mass% of gold = 31.66

mass% of silver =100-31.66 = 68.34