50g of steam at 100°C was passed into cold water at 20°C. The temperature on the water rose to 60°C…

Question

50g of steam at 100°C was passed into cold water at 20°C. The temperature on the water rose to 60°C. Determine the mass of cold water used (specific heat capacity of water = 4200J/KgK and specific latent heat of vapourisation of water = 2.26 × 106Jkg-1).

ScanSolve AI Tutor · Accepted Answer

Ili kutatua tatizo hili, tutatumia kanuni ya uhifadhi wa nishati, ambapo joto lililopotea na mvuke ni sawa na joto lililopatikana na maji baridi.

Badilisha wingi wa mvuke kutoka gramu kwenda kilogramu.
$m_s = 50 \text{ g} = \frac{50}{1000} \text{ kg} = 0.05 \text{ kg}$
Kokotoa joto lililopotea na mvuke wakati wa kufupisha (condensation) kutoka $100^\circ C$ hadi maji ya $100^\circ C$ .
Tunatumia fomula $Q = mL_v$ , ambapo $m$ ni wingi na $L_v$ ni joto maalum la mvukizo.
$Q_1 = m_s L_v = (0.05 \text{ kg}) \times (2.26 \times 10^6 \text{ J/Kg})$ $Q_1 = 113000 \text{ J}$
Kokotoa joto lililopotea na maji yaliyofupishwa (kutoka mvuke) wakati yanapoa kutoka $100^\circ C$ hadi $60^\circ C$ .
Tunatumia fomula $Q = mc\Delta T$ , ambapo $c$ ni uwezo maalum wa joto.
$\Delta T_s = 100^\circ C - 60^\circ C = 40^\circ C$ $Q_2 = m_s c_w \Delta T_s = (0.05 \text{ kg}) \times (4200 \text{ J/KgK}) \times (40 \text{ K})$ $Q_2 = 8400 \text{ J}$
Kokotoa jumla ya joto lililopotea na mvuke.
$Q_{iliyopotea} = Q_1 + Q_2 = 113000 \text{ J} + 8400 \text{ J}$ $Q_{iliyopotea} = 121400 \text{ J}$
Kokotoa joto lililopatikana na maji baridi wakati yanapashwa moto kutoka $20^\circ C$ hadi $60^\circ C$ .
Acha $m_w$ iwe wingi wa maji baridi.
$\Delta T_w = 60^\circ C - 20^\circ C = 40^\circ C$ $Q_{iliyopatikana} = m_w c_w \Delta T_w = m_w \times (4200 \text{ J/KgK}) \times (40 \text{ K})$ $Q_{iliyopatikana} = m_w \times 168000 \text{ J/Kg}$
Linganisha joto lililopotea na joto lililopatikana ( $Q_{iliyopotea} = Q_{iliyopatikana}$ ).
$121400 \text{ J} = m_w \times 168000 \text{ J/Kg}$ $m_w = \frac{121400 \text{ J}}{168000 \text{ J/Kg}}$ $m_w = \frac{1214}{1680} \text{ kg}$ $m_w \approx 0.7226 \text{ kg}$
Wingi wa maji baridi yaliyotumika ni takriban $0.723 \text{ kg}$ .
$\text{Wingi wa maji baridi} = \textbf{0.723 kg}$

50g of steam at 100°C was passed into cold water at 20°C. The temperature on the water rose to 60°C. Determine the mass of cold water used (specific heat capacity of water = 4200J/KgK and specific latent heat of vapourisation of water = 2.26 x 106Jkg-1).

Answer

Step-by-step solution

Badilisha wingi wa mvuke kutoka gramu kwenda kilogramu.

Kokotoa joto lililopotea na mvuke wakati wa kufupisha (condensation) kutoka $100^\circ C$ hadi maji ya $100^\circ C$ .

Kokotoa joto lililopotea na maji yaliyofupishwa (kutoka mvuke) wakati yanapoa kutoka $100^\circ C$ hadi $60^\circ C$ .

Kokotoa jumla ya joto lililopotea na mvuke.

Kokotoa joto lililopatikana na maji baridi wakati yanapashwa moto kutoka $20^\circ C$ hadi $60^\circ C$ .

Linganisha joto lililopotea na joto lililopatikana ( $Q_{iliyopotea} = Q_{iliyopatikana}$ ).

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