Question

Water has a specific heat capacity nearly nine times that of iron. Suppose a 50-g pellet of iron at a temperature of 200∘C is dropped into 50 g of water at a temperature of 20∘C.

When the system reaches thermal equilibrium, its temperature will be
a. closer to 20∘C.
b. halfway between the two initial temperatures.
c. closer to 200∘C.

Answer 1

a. closer to 20∘C

Step-by-step explanation:

`m_(p)` = mass of pallet = 50 g = 0.050 kg

`c_(p)` = specific heat of pallet = specific heat of iron

`T_(pi)` = Initial temperature of pellet = 200 C

`m_(w)` = mass of water = 50 g = 0.050 kg

`c_(w)` = specific heat of water

`T_(wi)` = Initial temperature of water = 20 C

`T_(e)` = Final equilibrium temperature

Also given that

`c_(w) = 9 c_(p)`

Using conservation of energy

Energy gained by water = Energy lost by pellet

`m_(w) c_(w) (T_(e) - T_(wi)) = m_(p) c_(p) (T_(pi) - T_(e))\\(0.050) (9) c_(p) (T_(e) - 20) = (0.050) c_(p) (200 - T_(e))\\ (9) (T_(e) - 20) =  (200 - T_(e))\\T_(e) = 38 C`

hence the correct choice is

a. closer to 20∘C