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Talja [164]
3 years ago
12

If you pour whisky over ice, the ice will cool the drink, but it will also dilute it. A solution is to use whisky stones. Suppos

e Ernest pours 55.0 g of whisky at 22 ∘C room temperature, and then adds three whisky stones to cool it. Each stone is a 32.0 g soapstone cube that is stored in the freezer at -11 ∘C. The specific heat of soapstone is 980 J/kg⋅K; the specific heat of whisky is 3400 J/kg⋅K.What is the final temperature of the whisky?
Physics
2 answers:
Ksenya-84 [330]3 years ago
8 0

Answer:

10.1 °C

Explanation:

After the mixture, heat is gained by the soapstone cubes (they were at a lower temperature) while heat is lost by the whisky (it was at a higher temperature).

Let the temperature of the mixture be <em>T</em>.

Heat lost by whisky, H_W = m_Wc_W\Delta\theta_W

m_W is the mass of the whisky (in kg), c_W is the specific heat of whisky (J/kg·K) and \Delta\theta_W is the change in temperature of the whisky (in °C or K).

H_W = (0.055\text{ kg})(3040\text{ J/kg}\cdot\text{K})(22-T) = 167.2(22-T) \text{ J}

Heat gained by soapstone cubes, H_C = m_Cc_C\Delta\theta_C

There are three cubes of soapstone, so their mass is multiplied by 3.

H_W = (3\times0.032\text{ kg})(980\text{ J/kg}\cdot\text{K})(T-(-11)) = 94.08(T+11) \text{ J}

From the principle of mixtures,

Heat lost by whisky = Heat gained by soapstone cubes (assuming no heat loss to the surroundings)

167.2(22-T) = 94.08(T+11)

3678.4 - 167.2T = 94.08T + 1034.88

2643.52 = 261.28T

T= 10.1

The final temperature of the whisky is 10.1 °C.

Anon25 [30]3 years ago
6 0

Answer: 11.0

Explanation: the heat capacity of the whiskey should be 3400 and not 3040

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