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A 300 g glass thermometer initially at 23 ◦C is put into 236 cm3 of hot water at 87 ◦C. Find the final temperature of the thermometer, assuming no heat flows to the surroundings. The specific heat of glass is 0.2 cal/g · ◦ C and of water 1 cal/g · ◦ C.

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lublana

Answer:

[tex]74^{\circ} C[/tex]

Explanation:

We are given that

Mass of glass,[tex]m=300 g[/tex]

[tex]T_1=23^{\circ}[/tex]

Volume,[tex]V=236cm^3[/tex]

Mass of water=[tex]density\times volume=1\times 236=236 g[/tex]

Density of water=[tex]1g/cm^3[/tex]

Temperature of hot water,[tex]T=87^{\circ}[/tex]

Specific heat of glass,[tex]C_g=0.2cal/g^{\circ}C[/tex]

Specific heat of water,[tex]C_w=1 cal/g^{\circ}C[/tex]

[tex]Q_{glass}=m_gC_g(T_f-T_1)=300\times 0.2(T_f-23)[/tex]

[tex]Q_{water}=m_wC_w(T_f-T)=236\times 1(T_f-87)[/tex]

[tex]Q_{glass}+Q_{water}=0[/tex]

[tex]300\times 0.2(T_f-23)+236\times 1(T_f-87)[/tex]

[tex]60T_f-1380+236T_f-20532=0[/tex]

[tex]296T_f=20532+1380=21912[/tex]

[tex]T_f=\frac{21912}{296}=74^{\circ} C[/tex]

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