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

Answer:

a. closer to 20∘C

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