This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Ili kutatua tatizo hili, tutatumia kanuni ya uhifadhi wa nishati, ambapo joto lililopotea na mvuke ni sawa na joto lililopatikana na maji baridi. Step 1: Badilisha wingi wa mvuke kutoka gramu kwenda kilogramu. m_s = 50 g = (50)/(1000) kg = 0.05 kg Step 2: Kokotoa joto lililopotea na mvuke wakati wa kufupisha (condensation) kutoka 100^ C hadi maji ya 100^ 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 kg) × (2.26 × 10^6 J/Kg) Q_1 = 113000 J Step 3: Kokotoa joto lililopotea na maji yaliyofupishwa (kutoka mvuke) wakati yanapoa kutoka 100^ C hadi 60^ C. Tunatumia fomula Q = mc T, ambapo c ni uwezo maalum wa joto. T_s = 100^ C - 60^ C = 40^ C Q_2 = m_s c_w T_s = (0.05 kg) × (4200 J/KgK) × (40 K) Q_2 = 8400 J Step 4: Kokotoa jumla ya joto lililopotea na mvuke. Q_iliyopotea = Q_1 + Q_2 = 113000 J + 8400 J Q_iliyopotea = 121400 J Step 5: Kokotoa joto lililopatikana na maji baridi wakati yanapashwa moto kutoka 20^ C hadi 60^ C. Acha m_w iwe wingi wa maji baridi. T_w = 60^ C - 20^ C = 40^ C Q_iliyopatikana = m_w c_w T_w = m_w × (4200 J/KgK) × (40 K) Q_iliyopatikana = m_w × 168000 J/Kg Step 6: Linganisha joto lililopotea na joto lililopatikana (Q_iliyopotea = Q_iliyopatikana). 121400 J = m_w × 168000 J/Kg m_w = 121400 J168000 J/Kg m_w = (1214)/(1680) kg m_w ≈ 0.7226 kg Wingi wa maji baridi yaliyotumika ni takriban 0.723 kg. Wingi wa maji baridi = 0.723 kg Tuma swali linalofuata 📸