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`