Question

Jaxon is making himself some instant noodles for lunch. He pours 130 g of water at 97°C into an insulating cup containing 86 g of noodles and 12 g of seasoning, both at room temperature (20°C). The specific heat capacity of water is 4200 J/kg°C, the specific heat capacity of the noodles is 1700 J/kg°C, and the specific heat capacity of the seasoning is 1300 J/kg°C. What is the final temperature of the mixture? Your answer should be in °C, but you do not need to type the unit in your final answer.

Answer 1

Answer:

The final temperature of the mixture = 79.4°C

Step-by-step explanation:

Mass of water, mw = 130g = 130/1000

mw = 0.13 kg

Initial temperature of the water, θw = 97°C

Let the final temperature of the mixture be θ

Specific capacity of water, cw = 4200 J/kg°C

Heat lost by the water

`\begin{gathered} H_w=m_wc_w(\theta_w-\theta) \\ \\ H_w=0.13(4200)(97-\theta) \\ \\ H_w=546(97-θ) \end{gathered}`

Mass of the noodles, mn = 86 g

mn = 86/1000 = 0.086 kg

Specific capacity of the noodles, cn = 1700 J/kg°C

Initial temperature of the noodles, θn = 20°C

Heat gained by the noodles

`\begin{gathered} H_n=m_nc_n(\theta-\theta_n) \\ \\ H_n=0.086(1700)(\theta-20) \\ \\ H_n=146.2(\theta-20) \end{gathered}`

Mass of the seasoning, ms = 12 g

ms = 12/1000 = 0.012 kg

Specific capacity of the noodles, cs = 1300 J/kg°C

Initial temperature of the noodles, θs = 20°C

Heat gained by the seasoning

`\begin{gathered} H_s=m_sc_s(\theta-\theta_s) \\ \\ H_s=0.012(1300)(\theta-20) \\ \\ H_s=15.6(\theta-20) \end{gathered}`
`\begin{gathered} H_s=m_sc_s(\theta-\theta_s) \\ \\ H_s=0.012(1300)(\theta-20) \\ \\ H_s=15.6(\theta-20) \end{gathered}`

Heat lost by the water = Heat gained by the noodles + Heat gained by the seasoning

`\begin{gathered} H_w=H_n+H_s \\ \\ 546(97-\theta)=146.2(\theta-20)+15.6(\theta-20) \\ \\ 52962-546\theta=146.2\theta-2924+15.6\theta-312 \\ \\ 146.2\theta+15.6\theta+546\theta=52962+2924+312 \\ \\ 707.8\theta=56198 \\ \\ \theta=(56198)/(707.8) \\ \\ \theta=79.4^oC \\ \end{gathered}`

The final temperature of the mixture = 79.4°C