Question #267073

Q 4. A 0.5 kg of aluminum cube at 27 ℃ and a 1.0 kg of copper cube at 100 ℃ are placed 

in 2 kg of water at 22 ℃. Assuming no heat loss to the surroundings, calculate the final 

temperature of the mixture.

Specific heat capacities: water 𝑐𝑊 = 4187 𝐽𝑘𝑔−1𝐾

−1

, copper 𝑐𝑐𝑢 = 386 𝐽𝑘𝑔−1𝐾

−1

aluminum 𝑐𝑎𝑙 = 900 𝐽𝑘𝑔−1𝐾

−1

Q 5. A 5 kg of ice cube at −10℃ is mixed with 0.1 kg of water at 80 ℃. There is no heat 

loss to the surrounding. The specific heat capacity of ice is 2.22 𝑘𝐽𝐾

−1𝑘𝑔−1

,The specific 

heat capacity of water is 4.187 𝑘𝐽𝐾

−1𝑘𝑔−1

. The specific latent heat of fusion of ice is 

333 𝑘𝐽 𝑘𝑔−1

.

(a) What is the final physical state of the mixture? (Gas, Liquid or Solid?)

Justify your answer using suitable calculations 

(b) What is the final temperature of the mixture?


1
Expert's answer
2021-11-17T08:30:58-0500

Q4. Let the final temperature o the mixture =x0Cx^0C

Heat lost by copper = heat gained by aluminium and water

mccc(100x)=mwcw(x22)+malcal(x27)m_cc_c(100-x)=m_wc_w(x-22)+m_{al}c_{al}(x-27)

1×386(100x)=2×4187(x22)+0.5×900(x27)1\times 386(100-x)=2\times 4187(x-22)+0.5\times 900(x-27)

38600386x=8374x184228+450x215038600-386x=8374x-184228+450x-2150

38600+184228+2150=386x+8374x+450x38600+184228+2150=386x+8374x+450x

234978=9210x234978=9210x

x=250Cx=25^0C


Q5. (a) Heat lost by water = heat gained by ice at -100C^0C +heat of fusion of ice +heat of melted ice (water)

Let the final temperature =x0Cx^0C

mwcw(80x)=micecice(x+10)+miceLf+mwcw(x0)m_wc_w(80-x)=m_{ice}c_{ice}(x+10)+m_{ice}L_f+m_{w}c_w(x-0)

0.1×4187(80x)=5×2220(x+10)+5×333000+5×4187(x)0.1\times 4187(80-x)=5\times 2220(x+10)+5\times 333000+5\times 4187(x)

33496418.7x=11100x+111000+1665000+20935x33496-418.7x=11100x+111000+1665000+20935x

32453.7x=1742504-32453.7x=1742504

x=53.690Cx=-53.69^0C

Final temperature is negative, so the mixture is a solid.

b) Final temperature is 53.690C53.69^0C


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