Example 2: how heat transferred depends on specific heat.

(a) How much heat input is needed to raise the temperature of an empty 20-kg vat made of iron from 10°C to 90°C? (b) What if the vat is filled with `20\ kg` of water? Given: `∆T = 90°C - 10°C=80\ C°` `m_i = 20\ kg` `m_w = 20\ kg` Known: `c_i = 450\ J//kg•C°` `c_w = 4186\ J//kg•C°` (a) `Q_(v a t) = m_i c_i∆T = (20\ kg)(450\ J//kg•C°)(80\ C°)`
`Q = 7.2 times 10^5\ J`
(b) `Q_(H_2O) = m_i c_i∆T = (20\ kg)(4186\ J//kg•C°)(80\ C°)` `Q_(H_2O) = 6.7 times 10^6\ J` `Q = Q_(v a t) +Q_(H_2O)`
`Q = 7.4 times 10^6\ J`