A coffee maker makes coffee by passing steam through a mixture of coffee powder, milk and water. If the steam is mixed at the rate of 50 g per minute in a mug containing 500 g of mixture, then it takes about t 0 seconds to make coffee at 70 ° C when the initial temperature of the mixture is 25 ° C . The value of t 0 is close to (ratio of latent heat of evaporation to specific heat of water is 540 ° C and specific heat of the mixture can be taken to be the same as that of water)

Question

A coffee maker makes coffee by passing steam through a mixture of coffee powder, milk and water. If the steam is mixed at the rate of 50 g per minute in a mug containing 500 g of mixture, then it takes about t 0 seconds to make coffee at 70 ° C when the initial temperature of the mixture is 25 ° C . The value of t 0 is close to (ratio of latent heat of evaporation to specific heat of water is 540 ° C and specific heat of the mixture can be taken to be the same as that of water), 30, 45, 60, 90

MARKS App · Accepted Answer

Let m gram of steam is condensed in the process of heating mixture from 25 ° C to 70 ° C Then, Heat lost by steam = Heat gained by mixture ⇒ Heat of condensation of steam + Heat given by water formed = Heat gained by mixture ⇒ m · L + m s w Δ T = M · s n Δ T = 500 × s w × ( 70 - 25 ) ⇒ m = 500 × s w × 45 L + 30 s w ⇒ m = 500 × 45 L s w + 30 ⇒ m = 500 × 45 ( 540 + 30 ) ≈ 40 g Now, in 1 min , 50 g of steam is condensed. ∴ 40 g of steam will be condensed in time t 0 t 0 = 40 × 60 50 s = 48 s Nearest answer is 45 s .

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