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 T.
Heat lost by whisky, [tex]H_W = m_Wc_W\Delta\theta_W[/tex]
[tex]m_W[/tex] is the mass of the whisky (in kg), [tex]c_W[/tex] is the specific heat of whisky (J/kg·K) and [tex]\Delta\theta_W[/tex] is the change in temperature of the whisky (in °C or K).
[tex]H_W = (0.055\text{ kg})(3040\text{ J/kg}\cdot\text{K})(22-T) = 167.2(22-T) \text{ J}[/tex]
Heat gained by soapstone cubes, [tex]H_C = m_Cc_C\Delta\theta_C[/tex]
There are three cubes of soapstone, so their mass is multiplied by 3.
[tex]H_W = (3\times0.032\text{ kg})(980\text{ J/kg}\cdot\text{K})(T-(-11)) = 94.08(T+11) \text{ J}[/tex]
From the principle of mixtures,
Heat lost by whisky = Heat gained by soapstone cubes (assuming no heat loss to the surroundings)
[tex]167.2(22-T) = 94.08(T+11)[/tex]
[tex]3678.4 - 167.2T = 94.08T + 1034.88[/tex]
[tex]2643.52 = 261.28T[/tex]
[tex]T= 10.1[/tex]
The final temperature of the whisky is 10.1 °C.
The final temperature is 10.95 °C.
When two bodies at different temperature come into contact, heat flows from the hotter body to the cooler body until thermal equilibrium is achieved between the two bodies.
Given that;
Heat lost by hot drink = Heat gained by whisky stones
Let the final temperature be θf
Heat lost by hot drink = mcθ
m = 55.0 g
c = 3400 J/kg⋅K
θ = 22 - θf
H = 55.0 × 3400 × (22 - θf)
Heat gained by whisky stones = mcθ
m = 3(32.0 g)
c = 980 J/kg⋅K
θ = θf - (-11)
H = 96 × 980 × (θf - (-11))
Hence;
55.0 × 3400 × (22 - θf) = 96 × 980 × (θf - (-11))
4114000 - 187000θf = 94080θf + 1034880
4114000 - 1034880 = 94080θf + 187000θf
3079120 = 281080θf
θf = 3079120/281080
θf = 10.95 °C
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