Question

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.

Answer 1

Answer:

$74^{\circ} C$

Explanation:

We are given that

Mass of glass,$m=300 g$

$T_1=23^{\circ}$

Volume,$V=236cm^3$

Mass of water=$density\times volume=1\times 236=236 g$

Density of water=$1g/cm^3$

Temperature of hot water,$T=87^{\circ}$

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

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

$Q_{glass}=m_gC_g(T_f-T_1)=300\times 0.2(T_f-23)$

$Q_{water}=m_wC_w(T_f-T)=236\times 1(T_f-87)$

$Q_{glass}+Q_{water}=0$

$300\times 0.2(T_f-23)+236\times 1(T_f-87)$

$60T_f-1380+236T_f-20532=0$

$296T_f=20532+1380=21912$

$T_f=\frac{21912}{296}=74^{\circ} C$