contestada

Temperature change time base problem. Suppose V = 24 V, I = 0.1 A, for water: mw = 51 gm, cw = 4.18 J/gm ∘K-1, for resistor: mr = 8 gm, and cr = 3.7 J/gm ∘K-1. If the water is initially at room temperature, how long will it take for the water to heat up 5∘K? (Hint: dT/dt is approximately equal to Δ T / Δt .)

Respuesta :

Answer:

[tex]t=5057.9167\ s[/tex]

Explanation:

Given:

  • Voltage supply to the resistor, [tex]V=24\ V[/tex]
  • current supply to the resistor, [tex]I=0.1\ A[/tex]
  • mass of water, [tex]m_w= 51\ g[/tex]
  • specific heat of water, [tex]c_w=4180\ J.kg^{-1}.K^{-1}[/tex]
  • specific heat of resistor, [tex]c_r=3700\ J.kg^{-1}.K^{-1}[/tex]
  • mass of resistor, [tex]m_r=0.008\ kg[/tex]
  • change in temperature, [tex]\Delta T=50\ K[/tex]

Now the amount of heat required to heat the water by 50 K:

[tex]Q_w=m_w.c_w.\Delta T[/tex]

[tex]Q_w=0.051\times 4180\times 50[/tex]

[tex]Q_w=10659\ J[/tex]

Now the amount of heat required to heat the resistor by 50 K:

[tex]Q_r=m_r.c_r.\Delta T[/tex]

[tex]Q_r=0.008\times 3700\times 50[/tex]

[tex]Q_r=1480\ J[/tex]

Now the total heat to converted from the electrical energy:

[tex]Q=Q_w+Q_r[/tex]

[tex]Q=12139\ J[/tex]

Now Using Joule's law of heating:

[tex]Q=V.I.t[/tex]

[tex]12139=24\times 0.1\times t[/tex]

[tex]t=5057.9167\ s[/tex]

The time taken to raise the temperature of the water by 5°K is 445.625 seconds.

Heat energy:

First, we calculate the total amount of heat required to raise the temperature of the water by 5°K,

[tex]\Delta Q=m_wc_w\Delta T[/tex]

where [tex]m_w[/tex] = 51gm is the mass of water

[tex]c_w[/tex] = 4.18 J/gK is the specific heat of the water

and ΔT = 5K is the change in temperature

so, the heat required is:

[tex]\Delta Q= 51\times4.18\times5\;J\\\\\Delta Q=1069.5\;J[/tex]

Now, the electrical energy generated by the circuit must be equal to the heat required, so:

E = ΔQ = V×I×t

where t is the time taken

V = 24 V is the potential difference, and

I = 0.1 A is the current

[tex]1069.5=24\times0.1\times t\\\\t=445.625\;s[/tex]

so the time taken is 445.625 s.

Learn more about specific heat:

https://brainly.com/question/2516072?referrer=searchResults

Otras preguntas

Q&A Education