If I submerge a hot iron rod with a mass of 1.8 kg, at 332 K and with a specific heat of 460 J/kgK in a bucket with an unknown mass of water at 252K of specific heat of 4200 J/kgK, until they are in thermal equilibrium at 280 K, what is the mass of the water in the bucket?

For this problem, we can assume that the heat gained and the heat lost are equal in magnitude, so we can set the two Q = mcΔT equations equal to one another. Thus we get, m_{iron} c_{iron} ΔT_{iron} = -m_{water} c_{water} ΔT_{water}, so we plug in all of the known values and get (1.8) (460) (52) = (28) (4200) m. Solving for m we get m = (1.8) (460) (520) / (280) (4200) = .366 kg