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You have a cup of tea (250 ml) that is 375 K which is too hot to drink. It needs to be cooled to 350 K before you can drink it. How much thermal energy has to be transferred from the tea to the surroundings to cool the tea? Show all work and include units.

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superman1987

Answer:

The hot tea should transfer 25.63 kJ the surroundings to cool the tea.

Explanation:

  • To solve this problem, we can use the relation:

Q = m.c.ΔT,

where, Q is the amount of heat has to be transferred from the tea to the surroundings to cool the tea (Q = ??? J).

m is the mass of the hot tea (m = dV = (1.0 g/mL)(250 mL) = 250 g), suppose the density of water is the density of tea.

c is the specific heat of the hot tea (c = 4.10 J/°C.g).

ΔT is the difference between the initial and final temperature (ΔT = final T - initial T = 350 K - 375 K = -25°C).

∴ Q = m.c.ΔT = (250 g)(4.10 J/°C.g)(-25°C)) = - 25630 J = - 25.63 kJ.

So, the hot tea should transfer 25.63 kJ the surroundings to cool the tea.

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