Question

Find the final temperature of the thermometer assuming no heat flows to the surroundings

Answer 1

`\begin{equation*} 71.51\degree C \end{equation*}`

Step-by-step explanation

Parameters given:

Mass of thermometer, m = 300 g

Initial temperature of thermometer, t1 = 35°C

Volume of water, V = 258 cm³

Initial temperature of water, T1 = 80°C

First, let us find the mass of the water using the formula for density:

`\begin{gathered} \rho=(M)/(V) \\ \Rightarrow M=\rho *V \end{gathered}`

where ρ = density of water = 1 g/cm³

Therefore, the mass of the water is:

`M=1*258=258g`

According to the conservation of energy, the total heat flow (the sum of the heat energy of the thermometer and water) must be equal to 0 since no heat flows to the surroundings:

`\begin{gathered} Q_g+Q_w=0 \\ mc(T-t_1)+MC(T-T_1)=0 \end{gathered}`

where c = specific heat capacity of glass thermometer = 0.2 cal/g°C

C = specific heat capacity of water = 1 cal/g°C

T = final temperature of thermometer and water

Hence, solving for T, we have that:

`\begin{gathered} T=(mct_1+MCT_1)/(mc+MC) \\ T=((300*0.2*35)+(258*1*80))/((300*0.2)+(258*1)) \\ T=(2100+20640)/(60+258)=(22740)/(318) \\ T=71.51\degree C \end{gathered}`

That is the final temperature of the thermometer.