More calculations on temperature and thermal equilibrium

Physics

ScanSolve AI Answer

Answer

34.33∘C34.33^\circ\text{C}

Step-by-step solution

4 steps

Here's another calculation problem on temperature and thermal equilibrium:

A 150 g150 \text{ g} aluminum block at 150∘C150^\circ\text{C} is submerged into 400 g400 \text{ g} of water at 25∘C25^\circ\text{C} in an insulated calorimeter. Determine the final equilibrium temperature of the mixture.

Given:

  • Specific heat capacity of aluminum (cAlc_{Al}) = 900 J/(kg⋅∘C)900 \text{ J/(kg}\cdot^\circ\text{C)}
  • Specific heat capacity of water (cwc_w) = 4186 J/(kg⋅∘C)4186 \text{ J/(kg}\cdot^\circ\text{C)}
  1. Convert masses to kilograms.

    mAl=150 g=0.150 kgm_{Al} = 150 \text{ g} = 0.150 \text{ kg} mw=400 g=0.400 kgm_w = 400 \text{ g} = 0.400 \text{ kg}
  2. Apply the principle of thermal equilibrium, where the heat lost by the aluminum equals the heat gained by the water.

    Qlost,Al=Qgained,wQ_{lost, Al} = Q_{gained, w}

    Using the formula Q=mcΔTQ = mc\Delta T, let TfT_f be the final equilibrium temperature.

    mAlcAl(TAl,i−Tf)=mwcw(Tf−Tw,i)m_{Al} c_{Al} (T_{Al,i} - T_f) = m_w c_w (T_f - T_{w,i})
  3. Substitute the given values into the equation.

    (0.150 kg)(900 J/(kg⋅∘C))(150∘C−Tf)=(0.400 kg)(4186 J/(kg⋅∘C))(Tf−25∘C)(0.150 \text{ kg})(900 \text{ J/(kg}\cdot^\circ\text{C)})(150^\circ\text{C} - T_f) = (0.400 \text{ kg})(4186 \text{ J/(kg}\cdot^\circ\text{C)})(T_f - 25^\circ\text{C})
  4. Simplify and solve for TfT_f.

    135(150−Tf)=1674.4(Tf−25)135 (150 - T_f) = 1674.4 (T_f - 25) 20250−135Tf=1674.4Tf−4186020250 - 135 T_f = 1674.4 T_f - 41860 20250+41860=1674.4Tf+135Tf20250 + 41860 = 1674.4 T_f + 135 T_f 62110=1809.4Tf62110 = 1809.4 T_f Tf=621101809.4T_f = \frac{62110}{1809.4} Tf≈34.33 ∘CT_f \approx 34.33 \text{ }^\circ\text{C}

    The final equilibrium temperature of the mixture is approximately 34.33∘C34.33^\circ\text{C}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp