Question

Suppose you have 500.0 grams of room temperature water (20 degrees celsius) in a thermos. You drop 150.0 grams of ice at 0 degrees celsius into the thermos and shut the lid. (a) what is the equilibrium temperature of the system? (b) how much ice is left (in grams)?

Answer 1

(a) we know, heat always flows higher temperature to lower temperature.

so, heat lost by water = heat gained by ice.

if we assume temperature of water drops to zero.

then, heat lost by water = ms∆T, where s is specific heat of water.

= 500gm × 1cal/gm.°C × (20°C - 0°C) = 10000 cal

now, heat gained by ice to melt = mLf , where Lf is latent heat of water.

= 150gm × 80cal/gm

= 12000 cal

here, it is clear that 12000 cal> 10000 cal

so, ice doesn't melt completely and hence, final temperature of water - ice system must be 0°C

hence, equilibrium temperature is 0°C.

(b) heat lost by water = mass of melted ice × latent heat of ice

or, 10000 Cal = m' × 80 cal/gm

or, m' = 10000/80 = 1000/8 = 125gm

hence, mass of remaining ice = 150 - 125 = 25gm